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A note on dimension of triangulated categories


Author: Hiroyuki Minamoto
Journal: Proc. Amer. Math. Soc. 141 (2013), 4209-4214
MSC (2010): Primary 16G60, 18E30
DOI: https://doi.org/10.1090/S0002-9939-2013-11723-5
Published electronically: September 6, 2013
MathSciNet review: 3105864
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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.


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Additional Information

Hiroyuki Minamoto
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email: minamoto@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2013-11723-5
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.

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