On generalized Beurling’s theorem and symmetry of -group algebras
Zenobia Anusiak (1971)
Colloquium Mathematicae
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Zenobia Anusiak (1971)
Colloquium Mathematicae
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Xinhong Chen, Ming Lu (2015)
Colloquium Mathematicae
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Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let and be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of . As a corollary, we find that if and only if if and only if .
Jan Waszkiewicz (1973)
Colloquium Mathematicae
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Philip Olin (1975)
Colloquium Mathematicae
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Helena Rasiowa
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Contents Introduction.................................................................................................................................................. 3 § 1. System of a propositional calculus...................................................................... 4 § 2. System ..................................................................................................................... 5 § 3. -algebras.....................................................................................................................
Igor Nikolaev (2015)
Czechoslovak Mathematical Journal
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The paper studies applications of -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension , and . In conclusion, we consider two numerical examples illustrating our main results.
Marius Dadarlat, Wilhelm Winter (2008)
Bulletin de la Société Mathématique de France
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Suppose is a separable unital -algebra each fibre of which is isomorphic to the same strongly self-absorbing and -injective -algebra . We show that and are isomorphic as -algebras provided the compact Hausdorff space is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.
Bjorn Poonen (2008)
Journal of the European Mathematical Society
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The moduli space of rank- commutative algebras equipped with an ordered basis is an affine scheme of finite type over , with geometrically connected fibers. It is smooth if and only if . It is reducible if (and the converse holds, at least if we remove the fibers above and ). The relative dimension of is . The subscheme parameterizing étale algebras is isomorphic to , which is of dimension only . For , there exist algebras that are not limits of étale algebras. The dimension...
Volker Runde (2003)
Studia Mathematica
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Let G be a locally compact group. We use the canonical operator space structure on the spaces for p ∈ [1,∞] introduced by G. Pisier to define operator space analogues of the classical Figà-Talamanca-Herz algebras . If p ∈ (1,∞) is arbitrary, then and the inclusion is a contraction; if p = 2, then OA₂(G) ≅ A(G) as Banach spaces, but not necessarily as operator spaces. We show that is a completely contractive Banach algebra for each p ∈ (1,∞), and that completely contractively...
Carlos Gallardo, Alicia Ziliani (2015)
Mathematica Bohemica
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T. Almada and J. Vaz de Carvalho (2001) stated the problem to investigate if these Łukasiewicz algebras are algebras of some logic system. In this article an affirmative answer is given and the -propositional calculus, denoted by , is introduced in terms of the binary connectives (implication), (standard implication), (conjunction), (disjunction) and the unary ones (negation) and , (generalized Moisil operators). It is proved that belongs to the class of standard systems...
Erhard Aichinger, Peter Mayr, R. McKenzie (2014)
Journal of the European Mathematical Society
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We prove that every clone of operations on a finite set , if it contains a Malcev operation, is finitely related – i.e., identical with the clone of all operations respecting for some finitary relation over . It follows that for a fixed finite set , the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra...
L.M. Camacho, B.A. Omirov, K.K. Masutova, I.M. Rikhsiboev (2017)
Open Mathematics
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All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.
J. Feinstein, D. Somerset (2000)
Studia Mathematica
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Let A be a unital Banach function algebra with character space . For , let and be the ideals of functions vanishing at x and in a neighbourhood of x, respectively. It is shown that the hull of is connected, and that if x does not belong to the Shilov boundary of A then the set has an infinite connected subset. Various related results are given.
Nathan Reading, David E. Speyer (2009)
Journal of the European Mathematical Society
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For a finite Coxeter group and a Coxeter element of ; the -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of . Its maximal cones are naturally indexed by the -sortable elements of . The main result of this paper is that the known bijection cl between -sortable elements and -clusters induces a combinatorial isomorphism of fans. In particular, the -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for...
Shiquan Ruan, Li Wang, Haicheng Zhang (2024)
Czechoslovak Mathematical Journal
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For any positive integer , let be a linearly oriented quiver of type with vertices. It is well-known that the quotient of an exact category by projective-injectives is an extriangulated category. We show that there exists an extriangulated equivalence between the extriangulated categories and , where and are the two extriangulated categories corresponding to the representation category of and the morphism category of projective representations of , respectively. As a...
A. Haldimann, H. Jarchow (2001)
Studia Mathematica
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The Nevanlinna algebras, , of this paper are the variants of classical weighted area Nevanlinna classes of analytic functions on = z ∈ ℂ: |z| < 1. They are F-algebras, neither locally bounded nor locally convex, with a rich duality structure. For s = (α+2)/p, the algebra of analytic functions f: → ℂ such that as |z| → 1 is the Fréchet envelope of . The corresponding algebra of analytic f: → ℂ such that is a complete metric space but fails to be a topological vector space....
Rüdiger Göbel, Saharon Shelah (2006)
Fundamenta Mathematicae
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An R-algebra A is called an E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra of the R-module , taking any a ∈ A to the right multiplication by a, is an isomorphism of algebras. In this case is called an E(R)-module. There is a proper class of examples constructed in [4]. E(R)-algebras arise naturally in various topics of algebra. So it is not surprising that they were investigated thoroughly in the last decades; see [3, 5, 7, 8, 10, 13, 14, 15, 18,...