The vanishing of self-extensions over n-symmetric algebras of quasitilted type

Maciej Karpicz; Marju Purin

Displaying similar documents to “The vanishing of self-extensions over n-symmetric algebras of quasitilted type”

Deformed mesh algebras of Dynkin type ℂₙ

Jerzy Białkowski, Karin Erdmann, Andrzej Skowroński (2012)

Colloquium Mathematicae

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In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type ₙ (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane singularities of Dynkin type $_{2 n}$ . In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type ℂₙ are isomorphic to the canonical mesh algebras of type ℂₙ, and hence to the stable...

Division algebras that generalize Dickson semifields

Daniel Thompson (2020)

Communications in Mathematics

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We generalize Knuth’s construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension $2 s^{2}$ by doubling central division algebras of degree $s$ . Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.

Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin (2010)

Banach Center Publications

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A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of $G^{\infty}$ -generalized functions class are given. A straightforward relationship between the classical and the generalized...

On a Construction of ModularGMS-algebras

Abd El-Mohsen Badawy (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety ${\underset{̲}{𝐊}}_{2}$ by means of ${\underset{̲}{K}}_{2}$ -quadruples. We also characterize isomorphisms of these algebras by means of ${\underset{̲}{K}}_{2}$ -quadruples.

Derived equivalences between generalized matrix algebras

QingHua Chen, HongJin Liu (2020)

Czechoslovak Mathematical Journal

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We construct derived equivalences between generalized matrix algebras. We record several corollaries. In particular, we show that the $n$ -replicated algebras of two derived equivalent, finite-dimensional algebras are also derived equivalent.

Generalized Post algebras and their application to some infinitary many-valued logics

Cat-Ho Nguyen

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CONTENTSIntroduction............................................................................................................................................................................... 5Part I. A generalization of Post algebras............................................................................................................................. 7 1. Definition and characterization of generalized Post algebras............................................. 7 2. Post...

Standardly stratified split and lower triangular algebras

Eduardo do N. Marcos, Hector A. Merklen, Corina Sáenz (2002)

Colloquium Mathematicae

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In the first part, we study algebras A such that A = R ⨿ I, where R is a subalgebra and I a two-sided nilpotent ideal. Under certain conditions on I, we show that A is standardly stratified if and only if R is standardly stratified. Next, for $A = [\begin{matrix} U & 0 \\ M & V \end{matrix}]$ , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and $_{V} M$ is a good V-module.

A geometric approach to full Colombeau algebras

R. Steinbauer (2010)

Banach Center Publications

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We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view of the construction of the intrinsically defined algebra $\hat{} (M)$ on the manifold M given in [gksv].

Skew-symmetric cluster algebras of finite mutation type

Anna Felikson, Michael Shapiro, Pavel Tumarkin (2012)

Journal of the European Mathematical Society

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In the famous paper [FZ2] Fomin and Zelevinsky obtained Cartan-Killing type classification of all cluster algebras of finite type, i.e. cluster algebras having only finitely many distinct cluster variables. A wider class of cluster algebras is formed by cluster algebras of finite mutation type which have finitely many exchange matrices (but are allowed to have infinitely many cluster variables). In this paper we classify all cluster algebras of finite mutation type with skew-symmetric...

Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2

Bruce Allison, Stephen Berman, Arturo Pianzola (2014)

Journal of the European Mathematical Society

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Let $𝕄_{n}$ be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to $n$ -tuples of commuting finite order automorphisms. It is a classical result that $𝕄_{1}$ is the class of all derived algebras modulo their centres of affine Kac-Moody Lie algebras. This combined with the Peterson-Kac conjugacy theorem for affine algebras results in a classification of the algebras in $𝕄_{1}$ . In this paper, we classify the algebras in $𝕄_{2}$ , and further determine the relationship between...

Metric generalizations of Banach algebras

W. Żelazko

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CONTENTSPRELIMINARIES§ 0. Introduction.......................................................................................................................................................................3§ 1. Definitions and notation.................................................................................................................................................5Chapter ILOCALLY BOUNDED ALGEBRAS§ 2. Basic facts and examples..............................................................................................................................................6§...

Some properties of orders of quaternion algebras with regard to the discrete norm

Jan Horníček, Miroslav Kureš, Lenka Macálková (2016)

Mathematica Bohemica

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Quaternion algebras $(\frac{- 1, b}{ℚ})$ are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.

The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach

Piotr Dowbor, Andrzej Mróz (2007)

Colloquium Mathematicae

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Given a module M over an algebra Λ and a complete set of pairwise nonisomorphic indecomposable Λ-modules, the problem of determining the vector $m (M) = {(m_{X})}_{X \in} \in ℕ^{}$ such that $M ≅ ⨁_{X \in} X^{m_{X}}$ is studied. A general method of finding the vectors m(M) is presented (Corollary 2.1, Theorem 2.2 and Corollary 2.3). It is discussed and applied in practice for two classes of algebras: string algebras of finite representation type and hereditary algebras of type $̃_{p, q}$ . In the second case detailed algorithms are given (Algorithms 4.5...

Some remarks on $Q$ -algebras

Nicolas Th. Varopoulos (1972)

Annales de l'institut Fourier

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We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that $ℓ^{p}$ , $(1 \leq p \leq \infty)$ are $Q$ algebras and that $A_{n} = ℨ L^{1} (Z; 1 + | n |^{α})$ is a $Q$ -algebra if and only if $α > 1 / 2$ .

Leibniz $A$ -algebras

David A. Towers (2020)

Communications in Mathematics

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A finite-dimensional Lie algebra is called an $A$ -algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras. ...

Beurling-Figà-Talamanca-Herz algebras

Serap Öztop, Volker Runde, Nico Spronk (2012)

Studia Mathematica

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For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras $A_{p} (G, ω)$ . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We...

Approximate amenability for Banach sequence algebras

H. G. Dales, R. J. Loy, Y. Zhang (2006)

Studia Mathematica

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We consider when certain Banach sequence algebras A on the set ℕ are approximately amenable. Some general results are obtained, and we resolve the special cases where $A = ℓ^{p}$ for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras $ℓ^{p} (ω)$ .