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Representability and autoequivalence groups

Part of: Homological methods Modules, bimodules and ideals Representation theory of rings and algebras

Published online by Cambridge University Press:  08 February 2021

XIAO–WU CHEN
XIAO–WU CHEN*
Affiliation:
Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Jinzhai Road No. 96, Hefei230026, Anhui, P.R. China. e-mail: xwchen@mail.ustc.edu.cn
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Abstract

For a finite dimensional algebra A, the bounded homotopy category of projective A-modules and the bounded derived category of A-modules are dual to each other via certain categories of locally-finite cohomological functors. We prove that the duality gives rise to a 2-categorical duality between certain strict 2-categories involving bounded homotopy categories and bounded derived categories, respectively. We apply the 2-categorical duality to the study of triangle autoequivalence groups.

MSC classification

Primary: 16E35: Derived categories
Secondary: 16G10: Representations of Artinian rings 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 171 , Issue 3 , November 2021 , pp. 657 - 668
Copyright
© Cambridge Philosophical Society 2021

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