Displaying similar documents to “Batalin-Vilkovisky algebra structures on Hochschild cohomology”

Rational BV-algebra in string topology

Yves Félix, Jean-Claude Thomas (2008)

Bulletin de la Société Mathématique de France

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Let M be a 1-connected closed manifold of dimension m and L M be the space of free loops on M . M.Chas and D.Sullivan defined a structure of BV-algebra on the singular homology of L M , H * ( L M ; k ) . When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology H H * ( C * ( M ) ; C * ( M ) ) which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between H H * ( C * ( M ) ; C * ( M ) ) and the shifted homology H * + m ( L M ; k ) . We also prove...

1 -cocycles on the group of contactomorphisms on the supercircle S 1 | 3 generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

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The relative cohomology H diff 1 ( 𝕂 ( 1 | 3 ) , 𝔬𝔰𝔭 ( 2 , 3 ) ; 𝒟 λ , μ ( S 1 | 3 ) ) of the contact Lie superalgebra 𝕂 ( 1 | 3 ) with coefficients in the space of differential operators 𝒟 λ , μ ( S 1 | 3 ) acting on tensor densities on S 1 | 3 , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1 -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1 -cocycle s ( X f ) = D 1 D 2 D 3 ( f ) α 3 1 / 2 , X f 𝕂 ( 1 | 3 ) which is invariant with respect to the conformal subsuperalgebra 𝔬𝔰𝔭 ( 2 , 3 ) of 𝕂 ( 1 | 3 ) . In this work we study the supergroup case. We give an explicit construction of 1 -cocycles...

A note on the cohomology ring of the oriented Grassmann manifolds G ˜ n , 4

Tomáš Rusin (2019)

Archivum Mathematicum

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We use known results on the characteristic rank of the canonical 4 –plane bundle over the oriented Grassmann manifold G ˜ n , 4 to compute the generators of the 2 –cohomology groups H j ( G ˜ n , 4 ) for n = 8 , 9 , 10 , 11 . Drawing from the similarities of these examples with the general description of the cohomology rings of G ˜ n , 3 we conjecture some predictions.

S -depth on Z D -modules and local cohomology

Morteza Lotfi Parsa (2021)

Czechoslovak Mathematical Journal

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Let R be a Noetherian ring, and I and J be two ideals of R . Let S be a Serre subcategory of the category of R -modules satisfying the condition C I and M be a Z D -module. As a generalization of the S - depth ( I , M ) and depth ( I , J , M ) , the S - depth of ( I , J ) on M is defined as S - depth ( I , J , M ) = inf { S - depth ( 𝔞 , M ) : 𝔞 W ˜ ( I , J ) } , and some properties of this concept are investigated. The relations between S - depth ( I , J , M ) and H I , J i ( M ) are studied, and it is proved that S - depth ( I , J , M ) = inf { i : H I , J i ( M ) S } , where S is a Serre subcategory closed under taking injective hulls. Some conditions are provided that local cohomology...

Matlis dual of local cohomology modules

Batoul Naal, Kazem Khashyarmanesh (2020)

Czechoslovak Mathematical Journal

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Let ( R , 𝔪 ) be a commutative Noetherian local ring, 𝔞 be an ideal of R and M a finitely generated R -module such that 𝔞 M M and cd ( 𝔞 , M ) - grade ( 𝔞 , M ) 1 , where cd ( 𝔞 , M ) is the cohomological dimension of M with respect to 𝔞 and grade ( 𝔞 , M ) is the M -grade of 𝔞 . Let D ( - ) : = Hom R ( - , E ) be the Matlis dual functor, where E : = E ( R / 𝔪 ) is the injective hull of the residue field R / 𝔪 . We show that there exists the following long exact sequence 0 H 𝔞 n - 2 ( D ( H 𝔞 n - 1 ( M ) ) ) H 𝔞 n ( D ( H 𝔞 n ( M ) ) ) D ( M ) H 𝔞 n - 1 ( D ( H 𝔞 n - 1 ( M ) ) ) H 𝔞 n + 1 ( D ( H 𝔞 n ( M ) ) ) H 𝔞 n ( D ( H ( x 1 , ... , x n - 1 ) n - 1 ( M ) ) ) H 𝔞 n ( D ( H ( n - 1 M ) ) ) ... , where n : = cd ( 𝔞 , M ) is a non-negative integer, x 1 , ... , x n - 1 is a regular sequence in 𝔞 on M and, for an R -module L , H 𝔞 i ( L ) is the i th local cohomology module...

On 1 -cocycles induced by a positive definite function on a locally compact abelian group

Jordan Franks, Alain Valette (2014)

Annales mathématiques Blaise Pascal

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For ϕ a normalized positive definite function on a locally compact abelian group G , let π ϕ be the unitary representation associated to ϕ by the GNS construction. We give necessary and sufficient conditions for the vanishing of 1-cohomology H 1 ( G , π ϕ ) and reduced 1-cohomology H ¯ 1 ( G , π ϕ ) . For example, H ¯ 1 ( G , π ϕ ) = 0 if and only if either Hom ( G , ) = 0 or μ ϕ ( 1 G ) = 0 , where 1 G is the trivial character of G and μ ϕ is the probability measure on the Pontryagin dual G ^ associated to ϕ by Bochner’s Theorem. This streamlines an argument of Guichardet...

Noetherian loop spaces

Natàlia Castellana, Juan Crespo, Jérôme Scherer (2011)

Journal of the European Mathematical Society

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The class of loop spaces of which the mod p cohomology is Noetherian is much larger than the class of p -compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as P and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space B X of such an object and prove it is as small as expected, that is, comparable to that of B P . We also show that B X differs basically from the classifying space of a p -compact...

Invariants, torsion indices and oriented cohomology of complete flags

Baptiste Calmès, Viktor Petrov, Kirill Zainoulline (2013)

Annales scientifiques de l'École Normale Supérieure

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Let  G be a split semisimple linear algebraic group over a field and let  T be a split maximal torus of  G . Let  𝗁 be an oriented cohomology (algebraic cobordism, connective K -theory, Chow groups, Grothendieck’s K 0 , etc.) with formal group law F . We construct a ring from F and the characters of  T , that we call a formal group ring, and we define a characteristic ring morphism c from this formal group ring to  𝗁 ( G / B ) where G / B is the variety of Borel subgroups of  G . Our main result says that when the...

Multiplicative Lie triple derivations on standard operator algebras

Bilal Ahmad Wani (2021)

Communications in Mathematics

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Let 𝒳 be a Banach space of dimension n > 1 and 𝔄 ( 𝒳 ) be a standard operator algebra. In the present paper it is shown that if a mapping d : 𝔄 𝔄 (not necessarily linear) satisfies d ( [ [ U , V ] , W ] ) = [ [ d ( U ) , V ] , W ] + [ [ U , d ( V ) ] , W ] + [ [ U , V ] , d ( W ) ] for all U , V , W 𝔄 , then d = ψ + τ , where ψ is an additive derivation of 𝔄 and τ : 𝔄 𝔽 I vanishes at second commutator [ [ U , V ] , W ] for all U , V , W 𝔄 . Moreover, if d is linear and satisfies the above relation, then there exists an operator S 𝔄 and a linear mapping τ from 𝔄 into 𝔽 I satisfying τ ( [ [ U , V ] , W ] ) = 0 for all U , V , W 𝔄 , such that d ( U ) = S U - U S + τ ( U ) for all U 𝔄 .

Cominimaxness of local cohomology modules

Moharram Aghapournahr (2019)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring, I an ideal of R . Let t 0 be an integer and M an R -module such that Ext R i ( R / I , M ) is minimax for all i t + 1 . We prove that if H I i ( M ) is FD 1 (or weakly Laskerian) for all i < t , then the R -modules H I i ( M ) are I -cominimax for all i < t and Ext R i ( R / I , H I t ( M ) ) is minimax for i = 0 , 1 . Let N be a finitely generated R -module. We prove that Ext R j ( N , H I i ( M ) ) and Tor j R ( N , H I i ( M ) ) are I -cominimax for all i and j whenever M is minimax and H I i ( M ) is FD 1 (or weakly Laskerian) for all i .

Hardness of embedding simplicial complexes in d

Jiří Matoušek, Martin Tancer, Uli Wagner (2011)

Journal of the European Mathematical Society

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Let 𝙴𝙼𝙱𝙴𝙳 k d be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k , does there exist a (piecewise linear) embedding of K into d ? Known results easily imply polynomiality of 𝙴𝙼𝙱𝙴𝙳 k 2 ( k = 1 , 2 ; the case k = 1 , d = 2 is graph planarity) and of 𝙴𝙼𝙱𝙴𝙳 k 2 k for all k 3 . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that 𝙴𝙼𝙱𝙴𝙳 d d and 𝙴𝙼𝙱𝙴𝙳 ( d - 1 ) d are undecidable for each d 5 . Our main result is NP-hardness of 𝙴𝙼𝙱𝙴𝙳 2 4 and, more generally, of 𝙴𝙼𝙱𝙴𝙳 k d for all...

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...

On the unit group of a semisimple group algebra 𝔽 q S L ( 2 , 5 )

Rajendra K. Sharma, Gaurav Mittal (2022)

Mathematica Bohemica

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We give the characterization of the unit group of 𝔽 q S L ( 2 , 5 ) , where 𝔽 q is a finite field with q = p k elements for prime p > 5 , and S L ( 2 , 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group 5 .

Involutivity degree of a distribution at superdensity points of its tangencies

Silvano Delladio (2021)

Archivum Mathematicum

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Let Φ 1 , ... , Φ k + 1 (with k 1 ) be vector fields of class C k in an open set U N + m , let 𝕄 be a N -dimensional C k submanifold of U and define 𝕋 : = { z 𝕄 : Φ 1 ( z ) , ... , Φ k + 1 ( z ) T z 𝕄 } where T z 𝕄 is the tangent space to 𝕄 at z . Then we expect the following property, which is obvious in the special case when z 0 is an interior point (relative to 𝕄 ) of 𝕋 : If z 0 𝕄 is a ( N + k ) -density point (relative to 𝕄 ) of 𝕋 then all the iterated Lie brackets of order less or equal to k Φ i 1 ( z 0 ) , [ Φ i 1 , Φ i 2 ] ( z 0 ) , [ [ Φ i 1 , Φ i 2 ] , Φ i 3 ] ( z 0 ) , ... ( h , i h k + 1 ) belong to T z 0 𝕄 . Such a property has been proved in [9] for k = 1 and its proof in the...