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REPETITIVE EQUIVALENCES AND TILTING THEORY

Part of: Homological methods Modules, bimodules and ideals Abelian categories General theory of categories and functors

Published online by Cambridge University Press:  06 December 2019

JIAQUN WEI
JIAQUN WEI*
Affiliation:
Department of Mathematics, Northwest Normal University, Lanzhou730070, China Institution of Mathematics, School of Mathematics Science, Nanjing Normal University, Nanjing210023, China email [email protected]
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Abstract

Let $R$ be a ring and $T$ be a good Wakamatsu-tilting module with $S=\text{End}(T_{R})^{op}$. We prove that $T$ induces an equivalence between stable repetitive categories of $R$ and $S$ (i.e., stable module categories of repetitive algebras $\hat{R}$ and ${\hat{S}}$). This shows that good Wakamatsu-tilting modules seem to behave in Morita theory of stable repetitive categories as that tilting modules of finite projective dimension behave in Morita theory of derived categories.

MSC classification

Primary: 18E10: Exact categories, abelian categories 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality 16E05: Syzygies, resolutions, complexes 16D20: Bimodules 18A25: Functor categories, comma categories 16E99: None of the above, but in this section
Type
Article
Information
Nagoya Mathematical Journal , Volume 243 , September 2021 , pp. 97 - 136
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Copyright
© 2019 Foundation Nagoya Mathematical Journal

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Footnotes

The author is supported by the Natural Science Foundation of China (Grant No. 11771212) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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