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arXiv · 1811.08992

The Differential Graded Stable Category of a Self-Injective Algebra

Jeremy Brightbill
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Abstract

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 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/$Ω$(1). This result allows computations in the dg-stable category to be performed by reducing to 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 dg-stable category of the Brauer tree algebra corresponding to the star with n edges.

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Jeremy Brightbill. 2019-07-18. The Differential Graded Stable Category of a Self-Injective Algebra. https://arxiv.org/abs/1811.08992

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