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

We fill a gap in the literature regarding 'transport of structure'for (n+ 2)-angulated, n-exact, n-
abelian and n-exangulated categories appearing in (classical and higher) homological …

Recollements of derived module categories are investigated, using a new technique,
ladders of recollements, which are maximal mutation sequences. The position in the ladder …

We construct some irreducible representations of the Leavitt path algebra of an arbitrary
quiver. The constructed representations are associated to certain algebraic branching …

This book is a lightly edited version of the unpublished manuscript Maximal Cohen–
Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz …

We introduce the notion of a perfect path for a monomial algebra. We classify
indecomposable non-projective Gorenstein-projective modules over the given monomial …

We determine the singularity category of an arbitrary finite‐dimensional gentle algebra Λ. It
is a finite product of n‐cluster categories of type A 1. Equivalently, it may be described as the …

Given an artin algebra $\Lambda $ with an idempotent element $ a $ we compare the
algebras $\Lambda $ and $ a\Lambda a $ with respect to Gorensteinness, singularity …

Let Q be a finite quiver with vertex set I and arrow set Q1, ka field, and kQ its path algebra
with its standard grading. This paper proves some category equivalences involving the …

We investigate necessary conditions for Gorenstein projective varieties to admit
semiorthogonal decompositions introduced by Kawamata, with main emphasis on threefolds …