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We give a complete description of all special biserial cluster-tilted algebras over a finite dimensional hereditary algebra H over an algebraically closed field K.
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We explicitly calculate a projective bimodule resolution for a special biserial algebra giving rise to the Hecke algebra when q = −1. We then determine the dimensions of the Hochschild cohomology groups. Mathematics Subject Class...
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We explicitly calculate a projective bimodule resolution for a special biserial algebra giving rise to the Hecke algebra when q = −1. We then determine the dimensions of the Hochschild cohomology groups. Mathematics Subject Classification (2000) 16E40 - 20C08 - 16E10(primary) Keywords Hochschild cohomology - Special biserial algebras - Hecke algebras The second author acknowledges support through an EPSRC Postdoctoral Fellowship EP/D077656/1 as well as through a Leverhulme Early Career Fellowship.
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We explicitly calculate a projective bimodule resolution for a special biserial algebra giving rise to the Hecke algebra H-q(S-4) when q = -1. We then determine the dimensions of the Hochschild cohomology groups.
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In this paper we give a new definition of symmetric special multiserial algebras in terms of defining cycles. As a consequence, we show that every special multiserial algebra is a quotient of a symmetric special multiserial algebr...
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In this paper we give a new definition of symmetric special multiserial algebras in terms of defining cycles. As a consequence, we show that every special multiserial algebra is a quotient of a symmetric special multiserial algebra. (C) 2016 Elsevier Inc. All rights reserved.
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Based on a four-term exact sequence, the formulae on the dimensions of the first and the second Hochschild cohomology groups of special biserial algebras with normed bases are obtained in terms of combinatorics.
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In this paper we study multiserial and special multiserial algebras. These algebras are a natural generalization of biserial and special biserial algebras to algebras of wild representation type. We define a module to be multiseri...
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In this paper we study multiserial and special multiserial algebras. These algebras are a natural generalization of biserial and special biserial algebras to algebras of wild representation type. We define a module to be multiserial if its radical is the sum of uniserial modules whose pairwise intersection is either 0 or a simple module. We show that all finitely generated modules over a special multiserial algebra are multiserial. In particular, this implies that, in analogy to special biserial algebras being biserial, special multiserial algebras are multiserial. We then show that the class of symmetric special multiserial algebras coincides with the class of Brauer configuration algebras, where the latter are a generalization of Brauer graph algebras. We end by showing that any symmetric algebra with radical cube zero is special multiserial and so, in particular, it is a Brauer configuration algebra. (C) 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license.
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We introduce the class of generalized biserial quiver algebras and prove that they provide a complete classification of all weakly symmetric biserial algebras over an algebraically closed field.
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Summary. We investigate the categorical behaviour of morphisms between indecomposable projective modules over a special biserial algebra A over an algebraically closed field, which are associated to arrows of the Gabriel quiver of A.
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We calculate the dimensions of the Hochschild cohomology groups of a self-injective special biserial algebra (s) obtained by a circular quiver with double arrows. Moreover, we give a presentation of the Hochschild cohomology ring ...
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We calculate the dimensions of the Hochschild cohomology groups of a self-injective special biserial algebra (s) obtained by a circular quiver with double arrows. Moreover, we give a presentation of the Hochschild cohomology ring modulo nilpotence of (s) by generators and relations. This result shows that the Hochschild cohomology ring modulo nilpotence of (s) is finitely generated as an algebra.
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We prove that the class of Brauer graph algebras coincides with the class of indecomposable idempotent algebras of biserial weighted surface algebras. These algebras are associated with triangulated surfaces with arbitrarily orien...
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We prove that the class of Brauer graph algebras coincides with the class of indecomposable idempotent algebras of biserial weighted surface algebras. These algebras are associated with triangulated surfaces with arbitrarily oriented triangles, investigated recently in Erdmann and Skowronski (J Algebra 505:490-558, 2018, Algebras of generalized dihedral type, Preprint. , 2017). Moreover, we prove that Brauer graph algebras are idempotent algebras of periodic weighted surface algebras, investigated in Erdmann and Skowronski (Algebras of generalized quaternion type, Preprint. , 2017).
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