A note on dimension of triangulated categories
H Minamoto - Proceedings of the American Mathematical Society, 2013 - ams.org
In this note we study the behavior of the dimension of the perfect derived category
$\operatorname {Perf}(A) $ of a dg-algebra $ A $ over a field $ k $ under a base field …
$\operatorname {Perf}(A) $ of a dg-algebra $ A $ over a field $ k $ under a base field …
On the finitistic dimension conjecture II: related to finite global dimension
C Xi - Advances in Mathematics, 2006 - Elsevier
In this paper, we study the finitistic dimensions of artin algebras by establishing a
relationship between the global dimensions of the given algebras, on the one hand, and the …
relationship between the global dimensions of the given algebras, on the one hand, and the …
The representation dimension of domestic weakly symmetric algebras
R Bocian, T Holm, A Skowroński - Central European Journal of …, 2004 - Springer
Auslander's representation dimension measures how far a finite dimensional algebra is
away from being of finite representation type. In [1], M. Auslander proved that a finite …
away from being of finite representation type. In [1], M. Auslander proved that a finite …
Extension dimensions: derived equivalences and stable equivalences
J Zhang, J Zheng - arXiv preprint arXiv:2210.05120, 2022 - arxiv.org
We show that the difference of the extension dimensions of two derived equivalent algebras
is bounded above by the minimal length of a tilting complex associated with a derived …
is bounded above by the minimal length of a tilting complex associated with a derived …
Tilting modules and dominant dimension with respect to injective modules
T Adachi, M Tsukamoto - The Quarterly Journal of Mathematics, 2021 - academic.oup.com
In this paper, we study a relationship between tilting modules with finite projective dimension
and dominant dimension with respect to injective modules as a generalization of results of …
and dominant dimension with respect to injective modules as a generalization of results of …
Split bounded extension algebras and Han's conjecture
Given a finite-dimensional algebra A over a field k, Han's conjecture relates two homological
invariants associated to A: its global dimension and its Hochschild homology. In the …
invariants associated to A: its global dimension and its Hochschild homology. In the …
Constructions of stable equivalences of Morita type for finite‐dimensional algebras III
Y Liu, C Xi - Journal of the London Mathematical Society, 2007 - Wiley Online Library
In this paper, we provide a new method to produce stable equivalences of Morita type. Our
main results can be stated as follows. Let A and B be two finite‐dimensional k‐algebras over …
main results can be stated as follows. Let A and B be two finite‐dimensional k‐algebras over …
Gelfand-Kirillov dimension and reducibility of scalar generalized Verma modules
ZQ Bai, W Xiao - Acta Mathematica Sinica, English Series, 2019 - Springer
Abstract The Gelfand-Kirillov dimension is an invariant which can measure the size of infinite-
dimensional algebraic structures. In this article, we show that it can also measure the …
dimensional algebraic structures. In this article, we show that it can also measure the …
[PDF][PDF] On the representation dimension of tilted and laura algebras
I Assem, MI Platzeck, SE Trepode - 2006 - ri.conicet.gov.ar
ON THE REPRESENTATION DIMENSION OF TILTED AND LAURA ALGEBRAS The chief
objective of the representation theory of artin algebras Page 1 ON THE REPRESENTATION …
objective of the representation theory of artin algebras Page 1 ON THE REPRESENTATION …