Results

**1 - 3**of**3**### MAPPING CONES IN THE BOUNDED DERIVED CATEGORY OF A GENTLE ALGEBRȦ

"... Abstract. Gentle algebras are a class of algebras that are derived tame. They therefore provide a concrete setting to study the structure of the (bounded) derived category in detail. In this article we explicitly describe the triangulated structure of the bounded derived category of a gentle algebr ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. Gentle algebras are a class of algebras that are derived tame. They therefore provide a concrete setting to study the structure of the (bounded) derived category in detail. In this article we explicitly describe the triangulated structure of the bounded derived category of a gentle algebra by describing its triangles. In particular, we develop a graphical calculus which gives the indecomposable summands of the mapping cones of morphisms in a canonical basis of the Hom-space between any two indecomposable complexes.

### 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

"... 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 ..."

Abstract
- Add to MetaCart

(Show Context)
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.