In this article, we initiate the study of hereditary extriangulated categories. Many important
categories arising in representation theory in connection with various theories of mutation …

We introduce higher dimensional analogues of the Nakayama algebras from the viewpoint
of Iyama's higher Auslander–Reiten theory. More precisely, for each Nakayama algebra A …

The symplectic geometry of higher Auslander algebras: Symmetric products of disks Page 1
Forum of Mathematics, Sigma (2021), Vol. 9:e10 1–49 doi:10.1017/fms.2021.2 RESEARCH …

This article consists of an introduction to Iyama's higher Auslander–Reiten theory for Artin
algebras from the viewpoint of higher homological algebra. We provide alternative proofs of …

For an exact category EE with enough projectives and with ad Z d Z-cluster tilting
subcategory, we show that the singularity category of EE admits ad Z d Z-cluster tilting …

For a higher Nakayama algebra $ A $ in the sense of Jasso-K\"{u} lshammer, we show that
the singularity category of $ A $ is triangulated equivalent to the stable module category of a …

We work over a perfect field. Recent work of the third-named author established a Derived
Auslander Correspondence that relates finite-dimensional self-injective algebras that are …

It is well known that for Auslander algebras, the category of all (finitely generated) projective
modules is an abelian category and this property of abelianness characterizes Auslander …

The aim of this thesis is to develop a localization theory in the higher homological algebra of
n-abelian and n-angulated categories. Analogously to the classical cases of an abelian or a …

Higher homological algebra, basically done in the framework of an $ n $-cluster tilting
subcategory $\mathcal {M} $ of an abelian category $\mathcal {A} $, has been the topic of …