The differential graded stable category of a self-injective algebra

[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/).

[发布日期] 2021-10-01

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