On representation-finite gendo-symmetric biserial algebras

A Chan, R Marczinzik - Algebras and Representation Theory, 2019 - Springer
algebras up to almost ν-stable derived equivalence by showing that the representative of each
equivalence … nant, global, and Gorenstein dimensions of these algebras. In particular, we …

On a conjecture about dominant dimensions of algebras

R Marczinzik - Journal of Algebra, 2021 - Elsevier
… An algebra is Gorenstein if injdim ( A ) = projdim ( D ( A ) ) < ∞ . In this case Gdim ( A ) : =
injdim ( A ) is the Gorenstein dimension of A and we say that A has infinite Gorenstein

[PDF][PDF] Tachikawa's second conjecture, derived recollements, and gendo-symmetric algebras

H Chen, M Fang, C Xi - wemath.cn
… -Gorenstein if and only if there is an algebra Λ and an (n−1)-… An A-module M is said to be
m-rigid if Exti A(M,M) = 0 for all 1 ≤ i ≤ m. Over symmetric algebras, ortho-symmetric modules

Fabric idempotents and higher Auslander-Reiten theory

J McMahon - Journal of Pure and Applied Algebra, 2020 - Elsevier
… In other words, for an algebra as above, we may consider any Gorenstein injective A-module
Fabric idempotents are quite natural, and we give multiple examples of algebras that admit …

Mirror-reflective algebras and Tachikawa's second conjecture

H Chen, M Fang, C Xi - arXiv preprint arXiv:2211.08037, 2022 - arxiv.org
… ) Auslander-Gorenstein algebras and gendo-symmetric algebras of … algebras are connected
by recollements of their derived … Over symmetric algebras, ortho-symmetric modules have …

Dominant Auslander-Gorenstein algebras and Koszul duality

A Chan, O Iyama, R Marczinzik - arXiv preprint arXiv:2210.06180, 2022 - arxiv.org
… of higher Auslader algebras as well as minimal AuslanderGorenstein algebras. We define
an algebra A to be dominant Auslander-Gorenstein if it is IwanagaGorenstein and idim P ≤ …

A higher dimensional Auslander-Iyama-Solberg correspondence

T Cruz, C Psaroudakis - arXiv preprint arXiv:2405.02736, 2024 - arxiv.org
… –Gorenstein algebras the module Q is both projective and injective. However, here, this
module … Observe also that Q fails to be an (1, 1)-ortho-symmetric module in the sense of [CK16] …

The combinatorics of tensor products of higher Auslander algebras of type A

J McMahon, NJ Williams - Glasgow Mathematical Journal, 2021 - cambridge.org
… , M is called a d-ortho-symmetric module M in [16]. For a d-preclustertilting module M, the …
Marczinzik, On minimal Auslander-Gorenstein algebras and standardly stratified algebras, J…

Rigidity dimensions of self-injective Nakayama algebras

W Hu, X Yin - arXiv preprint arXiv:2311.12697, 2023 - arxiv.org
equivalences by [3, Corolllary 5.4,], and a representation-finite self-injective algebra Λ of
type (Am-1,n/(m1),1) is derived equivalent to a self-injective Nakayama algebra with n simples …

Idempotent ideals and higher Auslander-Reiten theory/vorgelegt von Jordan McMahon

J McMahon - unipub.uni-graz.at
algebra is Iwanaga-Gorenstein. We show that tilted algebras of higher type A determine
higher gentle algebras, whereas this is not in true in general for the cluster-tilted algebras of A (…