Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on dimension of triangulated categories

Author: Hiroyuki Minamoto
Journal: Proc. Amer. Math. Soc. 141 (2013), 4209-4214
MSC (2010): Primary 16G60, 18E30
Published electronically: September 6, 2013
MathSciNet review: 3105864
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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 extension $ K/k$. In particular, we show that the dimension of a perfect derived category is invariant under a separable algebraic extension $ K/k$. As an application we prove the following statement: Let $ A$ be a self-injective algebra over a perfect field $ k$. If the dimension of the stable category $ \underline {\textrm {mod}}A$ is 0, then $ A$ is of finite representation type. This theorem is proved by M. Yoshiwaki in the case when $ k$ is an algebraically closed field. Our proof depends on his result.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 16G60, 18E30

Retrieve articles in all journals with MSC (2010): 16G60, 18E30

Additional Information

Hiroyuki Minamoto
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

Received by editor(s): April 25, 2011
Received by editor(s) in revised form: October 12, 2011, and February 22, 2012
Published electronically: September 6, 2013
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society