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The geometry of Brauer graph algebras and cluster mutations, (2014)

by R J Marsh, S Schroll
Venue:J. Algebra
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TRIVIAL EXTENSIONS OF GENTLE ALGEBRAS AND Brauer Graph Algebras

by Sibylle Schroll , 2014
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DERIVED EQUIVALENCES BETWEEN SYMMETRIC SPECIAL Biserial Algebras

by Takuma Aihara , 2014
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On the derived Picard group of . . .

by Alexandra Zvonareva , 2014
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Multiserial and special multiserial algebras and their representations 16G20 16D10 16D50 Keywords: Biserial Special biserial Radical cube zero Symmetric Multiserial Special multiserial Brauer configuration algebra

by E L Green , S
"... 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 inte ..."
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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.
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...ently there has been renewed interested in this class of algebras. On the one hand this interest stems from its connecting with cluster theory. In [5] the authors show that the Jacobian algebras of surface cluster algebras are gentle algebras, and hence a subclass of special biserial algebras. This class has been extensively studied since, see [21,35] for examples of the most recent results. On the other hand with the introduction of τ -tilting and silting theory [2,3], there has been a renewed interested in special biserial algebras and symmetric special biserial algebras, in particular, see [1,38,51,52]. For self-injective algebras, Brauer tree and Brauer graph algebras have been useful in the classification of group algebras and blocks of group algebras of finite and tame representation type [13,16,32,23] and the derived equivalence classification of self-injective algebras of tame representation type, see for example in [4,47] and the references within. In these classifications biserial and special biserial algebras have played an important role. In this paper, we study two classes of algebras, multiserial and special multiserial algebras introduced in [49], that are mostly of wild represe...

ALGEBRAS OF QUASI-QUATERNION TYPE

by unknown authors
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...n as a generalization of this statement to arbitrary triangulation quivers. We note that connections between Brauer graph algebras and cluster mutations have also been discovered by Marsh and Schroll =-=[22]-=-. For the two exceptional cases considered in Proposition 1.2, the statement (c′) holds since the corresponding triangulation algebras are of tubular type [2]. 6 SEFI LADKANI In part (d) we use the no...

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