[HTML][HTML] Upper bounds for the dominant dimension of Nakayama and related algebras
R Marczinzik - Journal of Algebra, 2018 - Elsevier
Optimal upper bounds are provided for the dominant dimensions of Nakayama algebras and
more general algebras A with an idempotent e such that there is a minimal faithful injective …
more general algebras A with an idempotent e such that there is a minimal faithful injective …
Quivers and the Adams spectral sequence
R Burklund, P Pstrągowski - arXiv preprint arXiv:2305.08231, 2023 - arxiv.org
In this paper, we describe a novel way of identifying Adams spectral sequence $ E_2 $-
terms in terms of homological algebra of quiver representations. Our method applies much …
terms in terms of homological algebra of quiver representations. Our method applies much …
Dominant Auslander-Gorenstein algebras and Koszul duality
A Chan, O Iyama, R Marczinzik - arXiv preprint arXiv:2210.06180, 2022 - arxiv.org
We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of
higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their …
higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their …
Derived and stable equivalences of centralizer matrix algebras
X Li, C Xi - arXiv preprint arXiv:2312.08794, 2023 - arxiv.org
The centralizer of a matrix in a full matrix algebra is called a principal centralizer matrix
algebra. Characterizations are presented for principal centralizer matrix algebras to be …
algebra. Characterizations are presented for principal centralizer matrix algebras to be …
Higher torsion-free Auslander-Reiten sequences and the dominant dimension of algebras
T Cruz, R Marczinzik - arXiv preprint arXiv:2404.02274, 2024 - arxiv.org
We generalise a theorem of Tachikawa about reflexive Auslander-Reiten sequences. We
apply this to give a new characterisation of the dominant dimension of gendo-symmetric …
apply this to give a new characterisation of the dominant dimension of gendo-symmetric …
A characterisation of Morita algebras in terms of covers
T Cruz - Algebras and Representation Theory, 2022 - Springer
Abstract A pair (A, P) is called a cover of End A (P) op if the Schur functor Hom A (P,−) is fully
faithful on the full subcategory of projective A-modules, for a given projective A-module P. By …
faithful on the full subcategory of projective A-modules, for a given projective A-module P. By …
Derived equivalences, restriction to self-injective subalgebras and invariance of homological dimensions
M Fang, W Hu, S Koenig - arXiv preprint arXiv:1607.03513, 2016 - arxiv.org
Derived equivalences between finite dimensional algebras do, in general, not pass to
centraliser (or other) subalgebras, nor do they preserve homological invariants of the …
centraliser (or other) subalgebras, nor do they preserve homological invariants of the …
Finitistic Auslander algebras
R Marczinzik - arXiv preprint arXiv:1701.00972, 2017 - arxiv.org
Recently, Chen and Koenig in\cite {CheKoe} and Iyama and Solberg in\cite {IyaSol}
independently introduced and characterised algebras with dominant dimension coinciding …
independently introduced and characterised algebras with dominant dimension coinciding …
Upper bounds for dominant dimensions of gendo-symmetric algebras
R Marczinzik - Archiv der Mathematik, 2017 - Springer
The famous Nakayama conjecture states that the dominant dimension of a non-selfinjective
finite dimensional algebra is finite. Yamagata (Frobenius algebras handbook of algebra, vol …
finite dimensional algebra is finite. Yamagata (Frobenius algebras handbook of algebra, vol …
On representation-finite gendo-symmetric algebras with only one non-injective projective module
T Aihara, A Chan, T Honma - Journal of Algebra, 2022 - Elsevier
Motivated by the relation between Schur algebra and the group algebra of a symmetric
group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen …
group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen …