The Ext algebra and a new generalisation of D-Koszul algebras

We generalise Koszul and D-Koszul algebras by introducing a class of graded algebras called (D,A)-stacked algebras. We give a characterisation of (D,A)-stacked algebras and show that their Ext algebra is finitely generated as an algebra in degrees 0, 1, 2 and 3. In the monomial case, we give an explicit description of the Ext algebra by quiver and relations, and show that the ideal of relations has a quadratic Gr\"obner basis; this enables us to give a regrading of the Ext algebra under which the regraded Ext algebra is a Koszul algebra.Comment: New title; minor changes; 25 page

A family of Koszul self-injective algebras with finite Hochschild cohomology

This paper presents an infinite family of Koszul self-injective algebras whose Hochschild cohomology ring is finite-dimensional. Moreover, for each $N \geq 5$ we give an example where the Hochschild cohomology ring has dimension $N$. This family of algebras includes and generalizes the 4-dimensional Koszul self-injective local algebras of Buchweitz, Green, Madsen and Solberg, which were used to give a negative answer to Happel's question, in that they have infinite global dimension but finite-dimensional Hochschild cohomology.Comment: 17 page

Group actions and coverings of Brauer graph algebras

We develop a theory of group actions and coverings on Brauer graphs that parallels the theory of group actions and coverings of algebras. In particular, we show that any Brauer graph can be covered by a tower of coverings of Brauer graphs such that the topmost covering has multiplicity function identically one, no loops, and no multiple edges. Furthermore, we classify the coverings of Brauer graph algebras that are again Brauer graph algebras.Comment: 26 pages Correction to statement of Theorem 6.7; a tower of coverings has been introduce

On Hochschild Cohomology of Preprojective Algebras, II

AbstractWe study the Hochschild cohomology of a finite-dimensional preprojective algebra; this is periodic by a result of A. Schofield. We determine the ring structure of the Hochschild cohomology ring given by the Yoneda product. As a result we obtain an explicit presentation by generators and relations