The differential graded stable category of a self-injective algebra

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Brightbill, Jeremy R. B.¹ 

[1] Univ Calif Santa Barbara, 552 Univ Rd, Santa Barbara, CA 93117 USA

关键词: Triangulated category;    Self-injective;    Brauer tree;    Differential graded algebra;   

DOI  :  10.1016/j.jpaa.2021.106708

来源: Elsevier

【 摘 要 】

Let A be a finite-dimensional, self-injective algebra, graded in non-positive degree. We define A -dgstab, the differential graded stable category of A, to be the Verdier quotient of the bounded derived category of dg-modules by the thick subcategory of perfect dg-modules. We express A -dgstab as the triangulated hull of the orbit category A -grstab /omega(1), reducing computations in the dg-stable category to those in the graded stable category. We provide a sufficient condition for the orbit category to be equivalent to A -dgstab and show this condition is satisfied by Nakayama algebras and Brauer tree algebras. We also provide a detailed description of the dgstable category of the Brauer tree algebra corresponding to the star with n edges. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

【 授权许可】

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