In representation theory of graded Iwanaga-Gorenstein algebras, tilting theory of the stable
category $\underline {\mathsf {CM}}^{\mathbb {Z}} A $ of graded Cohen-Macaulay modules …

We show that the Auslander-Reiten conjecture on stable equivalences holds true for
principal centralizer matrix algebras and for Frobenius-finite algebras over an algebraically …

We introduce the notion of relative hereditary Artin algebras, as a generalization of algebras
with representation dimension at most 3. We prove the following results.(1) The relative …

Important connections in representation theory arise from resolving a finite-dimensional
algebra by an endomorphism algebra of a generator-cogenerator with finite global …

Abstract∇-good filtration dimensions of modules and of algebras are introduced by Parker
for quasi-hereditary algebras. These concepts are now generalized to the setting of …

Let $\mathfrak {g} $ be a complex semisimple Lie algebra and $ U (\mathfrak {g}) $ be its
enveloping algebra. We deduce from the work of R. Bezrukavnikov, A. Braverman and L …

Throughout, let $ K $ be an algebraically closed field of characteristic $0 $. We provide a
generic classification of locally free representations of Geiss-Leclerc-Schr\" oer's algebras …

Let $ A $ be a Nakayama algebra with $ n $ simple modules and a simple module $ S $ of
even projective dimension. Choose $ m $ minimal such that a simple $ A $-module with …

We study the global dimensions of the coherent functors over two categories that are linked
by a pair of adjoint functors. This idea is then exploited to compare the representation …

Let A and B be two finite dimensional algebras over an algebraically closed field, related to
each other by a stable equivalence of Morita type. We prove that A and B have the same …