This book gives an introduction to the representation theory of finite groups and finite
dimensional algebras via homological algebra. In particular, it emphasises common …

Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting
complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an …

We give dual one-sided tilting complexes producing inverse equivalences of the derived
category of a Brauer star algebra and a Brauer tree algebra of the same type, folded …

In this paper we show that the derived Picard group TrPic (A) of the Brauer star algebra of
type (n, t) is generated by shift, Pic (A) and equivalences {H i} i= 1 n in the case t> 1, where H …

Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting
complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an …

It was shown in earlier work that every Brauer tree algebra of type (e, m) can be reached
from the Brauer star algebra of type (e, m) by a two-restricted tilting complex, ie, a complex …

In this paper we construct non-negative gradings on a basic Brauer tree algebra AΓ
corresponding to an arbitrary Brauer tree Γ of type (m, e). We do this by transferring gradings …

According to a result claimed by Pogorza_ly, selfinjective special biserial algebras can be
stably equivalent to stably biserial algebras only, and these two classes coincide. By an …

We consider the effect of performing an elementary equivalence as defined by Okuyama on
a group block of form $ F (C_p\times C_p)\rtimes C_r $, for a field $ F $ of characteristic $ p …

In this paper, all indecomposable two-term partial tilting complexes over a Brauer tree
algebra with multiplicity 1 are described, using a criterion for a minimal projective …