Displaying similar documents to “The Banach-Lie Group of Lie Automorphisms of an H * -Algebra”

Artinian automorphisms of infinite groups

Antonella Leone (2006)

Bollettino dell'Unione Matematica Italiana

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An automorphism a of a group G is called an artinian automorphism if for every strictly descending chain H 1 > H 2 > > H n > of subgroups of G there exists a positive integer m such that ( H n ) a = H n for every n m . In this paper we show that in many cases the group of all artinian automorphisms of G coincides with the group of all power automorphisms of G .

The groups of automorphisms of the Witt W n and Virasoro Lie algebras

Vladimir V. Bavula (2016)

Czechoslovak Mathematical Journal

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Let L n = K [ x 1 ± 1 , ... , x n ± 1 ] be a Laurent polynomial algebra over a field K of characteristic zero, W n : = Der K ( L n ) the Lie algebra of K -derivations of the algebra L n , the so-called Witt Lie algebra, and let Vir be the Virasoro Lie algebra which is a 1 -dimensional central extension of the Witt Lie algebra. The Lie algebras W n and Vir are infinite dimensional Lie algebras. We prove that the following isomorphisms of the groups of Lie algebra automorphisms hold: Aut Lie ( Vir ) Aut Lie ( W 1 ) { ± 1 } K * , and give a short proof that Aut Lie ( W n ) Aut K - alg ( L n ) GL n ( ) K * n .

The Schreier Property and Gauss' Lemma

Daniel D. Anderson, Muhammad Zafrullah (2007)

Bollettino dell'Unione Matematica Italiana

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Let D be an integral domain with quotient field D . Recall that D is Schreier if D is integrally closed and for all x , y , z D { 0 } , x | y z implies that x = r s where r | y e s | z . A GCD domain is Schreier. We show that an integral domain D is a GCD domain if and only if (i) for each pair a , b D { 0 } , there is a finitely generated ideal B such that a D b D = B v and (ii) every quadratic in D [ X ] that is a product of two linear polynomials in K [ X ] is a product of two linear polynomials in D [ X ] . We also show that D is Schreier if and only if every...

-homomorphisms of Lie algebras

Aleksander A. Lashkhi (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si studiano gli omomorfismi reticolari ( -omomorfismi) di algebre di Lie sopra anelli commutativi con unità. Le algebre di Lie sopra un campo e le p -algebre di Lie non ammettono -omomorfismi propri. Si assegnano condizioni necessarie e sufficienti affinchè un'algebra di Lie periodica o mista possieda un « -omomorfismo su una catena di lunghezza n .

Eisenstein ideal and reducible λ -adic Representations Unramified Outside a Finite Number of Primes.

Miriam Ciavarella (2006)

Bollettino dell'Unione Matematica Italiana

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The object of this note is to study certain 2-dimensional λ -adic representations of Gal ( Q ¯ / Q ) ; fixed p 1 , , p n distinct primes, we will consider representations ρ : G G L 2 ( A ) , given by the matrix ρ = ( a b c d ) which are unramified outside p 1 , , p n , and the residue characteristic of λ , which are a product of m representations over finite extensions of the ring of Witt vectors of the residue field and which are reducible modulo λ . In analogy with the theory of the modular representations, we will introduce the analogue of Mazur's Hecke...

A Montel Type Result for Subharmonic Functions

R. Supper (2009)

Bollettino dell'Unione Matematica Italiana

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This article is devoted to sequences ( u n ) n of subharmonic functions in N , with finite order, whose means J u n ( r ) (over spheres centered at the origin, with radius r) satisfy such a condition as: r > 0 , A r > 0 such that J u n ( r ) A r , n 𝐍 . The paper investigates under which conditions one may extract a pointwise or uniformly convergent subsequence.

Congruences between modular forms and related modules

Miriam Ciavarella (2006)

Bollettino dell'Unione Matematica Italiana

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We fix a prime and let M be an integer such that M ; let f S 2 ( Γ 1 ( M 2 ) ) be a newform supercuspidal of fixed type at and special at a finite set of primes. For an indefinite quaternion algebra over Q , of discriminant dividing the level of f , there is a local quaternionic Hecke algebra T associated to f . The algebra T acts on a module M f coming from the cohomology of a Shimura curve. Applying the Taylor-Wiles criterion and a recent Savitt's theorem, T is the universal deformation ring of a global...

Isomorphisms of Royden Type Algebras Over 𝕊 1

Teresa Radice, Eero Saksman, Gabriella Zecca (2009)

Bollettino dell'Unione Matematica Italiana

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Let 𝕊 1 and 𝔻 be the unit circle and the unit disc in the plane and let us denote by 𝒜 ( 𝕊 1 ) the algebra of the complex-valued continuous functions on 𝕊 1 which are traces of functions in the Sobolev class W 1 , 2 ( 𝔻 ) . On 𝒜 ( 𝕊 1 ) we define the following norm u = u L ( 𝕊 1 ) + ( 𝔻 | u ~ | 2 ) 1 / 2 where is the harmonic extension of u to 𝔻 . We prove that every isomorphism of the functional algebra 𝒜 ( 𝕊 1 ) is a quasitsymmetric change of variables on 𝕊 1 .

Correctors for Parabolic Equations in a Heterogeneous Fibered Medium

Mourad Sfaxi, Ali Sili (2007)

Bollettino dell'Unione Matematica Italiana

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We study the problem of correctors in the framework of the homogenization of linear parabolic equations posed in a heterogeneous medium Ω made of two materials. The first one is located in a set F ϵ of cylindrical parallel fibers periodically distributed with a period of size ϵ , and the second one is located in the "matrix" M ϵ = Ω F ϵ . The ratio between the conductivity coefficients of the two materials is of order 1 / ϵ 2 . After writing the homogenized problem, we give a corrector result and prove...

A New L 1 -Lower Semicontinuity Result

Daniele Graziani (2007)

Bollettino dell'Unione Matematica Italiana

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The aim of this work is to prove a chain rule and an L 1 -lower semicontinuity theorems for integral functional defined on B V ( Ω ) . Moreover we apply this result in order to obtain new relaxation and Γ -convergence result without any coerciveness and any continuity assumption of the integrand f ( x , s , p ) with respect to the variable s .

On the projective genus of surfaces

Pietro Sabatino (2006)

Bollettino dell'Unione Matematica Italiana

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Let X N be a smooth irreducible non degenerate surface over the complex numbers, N 4 . We define the projective genus of X , denoted by P G ( X ) , as the geometric genus of the singular curve of the projection of X from a general linear subspace of codimension four. Denote by g ( X ) the sectional genus of X . In this paper we conjecture that the only surfaces for which P G ( X ) = g ( X ) - 1 are the del Pezzo surface in 4 , in 5 and a conic bundle of degree 5 in 4 . We prove that for N 5 if P G ( X ) = g ( X ) - 1 + λ , λ a non negative integer, then g ( X ) λ + 1 + α where...

On automorphisms of the Banach space / c

Piotr Koszmider, Cristóbal Rodríguez-Porras (2016)

Fundamenta Mathematicae

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We investigate Banach space automorphisms T : / c / c focusing on the possibility of representing their fragments of the form T B , A : ( A ) / c ( A ) ( B ) / c ( B ) for A,B ⊆ ℕ infinite by means of linear operators from ( A ) into ( B ) , infinite A×B-matrices, continuous maps from B* = βB∖B into A*, or bijections from B to A. This leads to the analysis of general bounded linear operators on / c . We present many examples, introduce and investigate several classes of operators, for some of them we obtain satisfactory representations and for...

Some Separation Axioms Via Ideals

D. Sivaraj, V. Renuka Devi (2007)

Bollettino dell'Unione Matematica Italiana

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We introduce a new class of spaces, called Hausdorff modulo or T 2 mod spaces with respect to an ideal which contains the class of all Hausdorff spaces. Characterizations of these spaces are given and their properties are investigated. The concept of compactness modulo an ideal was introduced by Newcomb in 1967 and studied by Hamlett and Jankovic in 1990. We study the properties of -compact subsets in Hausdorff modulo spaces and generalize some results of Hamlett and Jankovic....

Convergence to Equilibrium of the Solution of Kac's Kinetic Equation. A Probabilistic View

Eugenio Regazzini (2009)

Bollettino dell'Unione Matematica Italiana

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Let f ( , t ) be the probability density function representing the solution of Kac's Boltzmann-like equation at time t , with initial data f 0 , and let g σ be the Gaussian density with zero mean and variance σ 2 , σ 2 being the value of the second moment of f 0 . Henry McKean Jr. put forward the conjecture that the total variation distance between f ( , t ) and g σ goes to zero, as t + , with an exponential rate equal to - 1 / 4 . This lecture aims at explaining the main efforts made to a view to validating this conjecture,...

Polycyclic groups with automorphisms of order four

Tao Xu, Fang Zhou, Heguo Liu (2016)

Czechoslovak Mathematical Journal

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In this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if α is an automorphism of order four of a polycyclic group G and the map ϕ : G G defined by g ϕ = [ g , α ] is surjective, then G contains a characteristic subgroup H of finite index such that the second derived subgroup H ' ' is included in the centre of H and C H ( α 2 ) is abelian, both C G ( α 2 ) and G / [ G , α 2 ] are abelian-by-finite. These results extend recent and classical results in...

Cohomology of Tango bundle on 5

Daniele Faenzi (2006)

Bollettino dell'Unione Matematica Italiana

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The Tango bundle T is defined as the pull-back of the Cayley bundle over a smooth quadric Q 5 in 6 via a map f existing only in characteristic 2 and factorizing the Frobenius φ . The cohomology of T is computed in terms of S C , φ * ( C ) , Sym 2 ( C ) and C , which we handle with Borel-Bott-Weil theorem.

Relaxation and gamma-convergence of supremal functionals

Francesca Prinari (2006)

Bollettino dell'Unione Matematica Italiana

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We prove that the Γ -limit in L μ of a sequence of supremal functionals of the form F k ( u ) = μ - ess sup Ω f k ( x , u ) is itself a supremal functional. We show by a counterexample that, in general, the function which represents the Γ -lim F ( , B ) of a sequence of functionals F k ( u , B ) = μ - ess sup B f k ( x , u ) can depend on the set B and wegive a necessary and sufficient condition to represent F in the supremal form F ( u , B ) = μ - ess sup B f ( x , u ) . As a corollary, if f represents a supremal functional, then the level convex envelope of f represents its weak* lower semicontinuous envelope. ...

A Note on Sectorial and R-Sectorial Operators

Alberto Venni (2008)

Bollettino dell'Unione Matematica Italiana

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The following results are proved: (i) if α , β + and A is a sectorial operator, then the set { t α A β ( t + A ) ; t > 0 } is bounded; (ii) the same set of operators is R-bounded if A is R-sectorial.

A Regular Threefold of General Type with p g = 0 and P 2 = 6

M. Cristina Ronconi (2009)

Bollettino dell'Unione Matematica Italiana

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The range of the bigenus P 2 is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with p g = 0 : The examples in the literature have P 2 5 . In the present paper we present a non-singular threefold with p g = q 1 = q 2 = 0 ; P 2 = 6 ; the bicanonical map is stably birational.

Connected Components of Hurwitz Spaces of Coverings with One Special Fiber and Monodromy Groups Contained in a Weyl Group of Type B d

Francesca Vetro (2008)

Bollettino dell'Unione Matematica Italiana

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Let X , X , Y be smooth projective complex curves with Y curve of genus 1 . Let d be an integer 3 , let e ¯ = ( e 1 , , e r ) be a partition of d and let | e | = i = 1 r ( e i - 1 ) . Let X 𝜋 X 𝑓 Y be a sequence of coverings where π is a degree 2 branched covering and f is a degree d covering, with monodromy group S d , branched in n 2 + 1 points, one of which is special point c whose local monodromy has cycle type given by e ¯ . Moreover the branch locus of the covering π is contained in f - 1 ( c ) . In this paper we prove the irreducibility...

The group of automorphisms of L is algebraically reflexive

Félix Cabello Sánchez (2004)

Studia Mathematica

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We study the reflexivity of the automorphism (and the isometry) group of the Banach algebras L ( μ ) for various measures μ. We prove that if μ is a non-atomic σ-finite measure, then the automorphism group (or the isometry group) of L ( μ ) is [algebraically] reflexive if and only if L ( μ ) is *-isomorphic to L [ 0 , 1 ] . For purely atomic measures, we show that the group of automorphisms (or isometries) of ( Γ ) is reflexive if and only if Γ has non-measurable cardinal. So, for most “practical” purposes, the automorphism...

Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra

Liufeng Cao, Dong Su, Hua Yao (2023)

Czechoslovak Mathematical Journal

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Let r ( 𝔴 2 0 ) be the Green ring of the weak Hopf algebra 𝔴 2 0 corresponding to Sweedler’s 4-dimensional Hopf algebra H 2 , and let Aut ( R ( 𝔴 2 0 ) ) be the automorphism group of the Green algebra R ( 𝔴 2 0 ) = r ( 𝔴 2 0 ) . We show that the quotient group Aut ( R ( 𝔴 2 0 ) ) / C 2 S 3 , where C 2 contains the identity map and is isomorphic to the infinite group ( * , × ) and S 3 is the symmetric group of order 6.

Conductor and separating degrees for sets of points in r and in 1 × 1

Lucia Marino (2006)

Bollettino dell'Unione Matematica Italiana

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We attempt to generalize conductor degree's results, known in 2 , to the case of 0-dimensional schemes of r . In the first part of this paper, we consider the problem of characterizing the sequences generators's degrees of the conductor which are compatible with a fixed postulation (or Hilbert function) for a set of points in r and we determine the conductor degree of every point in a r -partial intersection. In addition, we define the separating degree of a point for a 0-dimensional subscheme...

Geometry of Syzygies via Poncelet Varieties

Giovanna Ilardi, Paola Supino, Jean Vallès (2009)

Bollettino dell'Unione Matematica Italiana

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We consider the Grassmannian 𝔾 r ( k , n ) of ( k + 1 ) -dimensional linear subspaces of V n = H 0 ( 1 , 𝒪 1 ( n ) ) . We define 𝔛 k , r , d as the classifying space of the k -dimensional linear systems of degree n on 1 , whose bases realize a fixed number r of polynomial relations of fixed degree d , say r syzygies of degree d . Firstly, we compute the dimension of 𝔛 k , r , d . In the second part we make a link between 𝔛 k , r , d and the Poncelet varieties. In particular, we prove that the existence of linear syzygies implies the existence of singularities on the...

Projection of Wreath Products of Lie Algebras

Alexander A. Lašhi (1980)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Sia K un dominio a ideali principali, che non sia un campo e sia L un'algebra di Lie su K . Principale risultato: Se L = A w r B , cioè se L è prodotto intrecciato delle algebre di Lie precarie A e B , ogni isomorfismo reticolare normale di L è indotto da un isomorfismo. Si prova anche, mediante un esempio, che per le algebre sopra un campo il teorema non è vero.

Coleman automorphisms of finite groups with a self-centralizing normal subgroup

Jinke Hai (2020)

Czechoslovak Mathematical Journal

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Let G be a finite group with a normal subgroup N such that C G ( N ) N . It is shown that under some conditions, Coleman automorphisms of G are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings.

A Result About C 2 -Rectifiability of One-Dimensional Rectifiable Sets. Application to a Class of One-Dimensional Integral Currents

Silvano Delladio (2007)

Bollettino dell'Unione Matematica Italiana

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Let γ , τ : [ a , b ] R k + 1 be a couple of Lipschitz maps such that γ = ± | γ | τ almost everywhere in [ a , b ] . Then γ ( [ a , b ] ) is a C 2 -rectifiable set, namely it may be covered by countably many curves of class C 2 embedded in R k + 1 . As a conseguence, projecting the rectifiable carrier of a one-dimensional generalized Gauss graph provides a C 2 -rectifiable set.

Threefolds with Kodaira Dimension 0 or 3

Ezio Stagnaro (2007)

Bollettino dell'Unione Matematica Italiana

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Using the theory of adjoints and pluricanonical adjoints, we construct three nonsingular threefolds, as desingularizations of degree six hypersurfaces in 4 , having the irregularities q 1 = q 2 = 0 and the following periodical sequences of plurigenera respectively ( p g , P 2 , P 3 , , P m , ) = ( 0 , 0 , 1 , 0 , 0 , 1 , ) , ( 0 , 0 , 0 , 1 , 0 , 0 , 0 , 1 , ) , ( 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 1 , ) . In the Appendix, starting from the second above-mentioned example, we construct a threefold of general type with q q 1 = q 2 = 0 , p g = 1 , P 2 = 2 whose m-canonical transformation is birational if and only if m 11 .

A note on singular and degenerate abstract equations

Angelo Favini (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Si considera l’equazione astratta B A 1 u + A 0 u = h , dove A i ( i = 0 , 1 ) e B sono convenienti operatori lineari chiusi fra spazi di Banach, A i non è necessariamente invertibile, e A 0 , A 1 non commutano con B . Si studiano esistenza ed unicità delle soluzioni. Si indicano alcune applicazioni a certe equazioni differenziali degeneri o singolari.

Squarefree Lexsegment Ideals with Linear Resolution

Vittoria Bonanzinga, Loredana Sorrenti (2008)

Bollettino dell'Unione Matematica Italiana

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In this paper we determine all squarefree completely lexsegment ideals which have a linear resolution. Let M d denote the set of all squarefree monomials of degree d in a polynomial ring k [ x 1 , , x n ] in n variables over a field k . We order the monomials lexicographically such that x 1 > x 2 > > x n , thus a lexsegment (of degree d ) is a subset of M d of the form L ( u , v ) = { w M d : u w v } for some u , v M d con u v . An ideal generated by a lexsegment is called a lexsegment ideal. We describe the procedure to determine when such an ideal has a linear...

On the Dirichlet Problem with Orlicz Boundary Data

Gabriella Zecca (2007)

Bollettino dell'Unione Matematica Italiana

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Let us consider a Young's function Φ : + + satisfying the Δ 2 condition together with its complementary function Ψ , and let us consider the Dirichlet problem for a second order elliptic operator in divergence form: { L u = 0 in  B u | B = f B the unit ball of n . In this paper we give a necessary and sufficient condition for the L ϕ -solvability of the problem, where L ϕ is the Orlicz Space generated by the function Φ . This means solvability for f L Φ in the sense of [5], [8], where the case Φ ( t ) = t p is treated. ...

The Martingale Problem in Hilbert Spaces

Giuseppe Da Prato, Luciano Tubaro (2008)

Bollettino dell'Unione Matematica Italiana

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We consider an SPDE in a Hilbert space H of the form d X ( t ) = ( A X ( t ) + b ( X ( t ) ) ) d t + σ ( X ( t ) ) d W ( t ) , X ( 0 ) = x H and the corresponding transition semigroup P t f ( x ) = 𝔼 [ f ( X ( t , x ) ) ] . We define the infinitesimal generator L ¯ of P t through the Laplace transform of P t as in [1]. Then we consider the differential operator L φ = 1 2 Tr [ σ ( x ) σ * ( x ) D 2 φ ] + b ( x ) , D φ defined on a suitable set V of regular functions. Our main result is that if V is a core for L ¯ , then there exists a unique solution of the martingale problem defined in terms of L . Application to the Ornstein-Uhlenbeck equation and to some regular...

A note on singular and degenerate abstract equations

Angelo Favini (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Si considera l’equazione astratta B A 1 u + A 0 u = h , dove A i ( i = 0 , 1 ) e B sono convenienti operatori lineari chiusi fra spazi di Banach, A i non è necessariamente invertibile, e A 0 , A 1 non commutano con B . Si studiano esistenza ed unicità delle soluzioni. Si indicano alcune applicazioni a certe equazioni differenziali degeneri o singolari.