2018
DOI: 10.48550/arxiv.1811.08992
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The Differential Graded Stable Category of a Self-Injective Algebra

Abstract: Let A be a finite-dimensional, self-injective algebra, graded in nonpositive 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 … Show more

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Cited by 1 publication
(9 citation statements)
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“…We define the differential graded stable category of A to be A -dgstab := D b dg (A)/D perf dg (A). The basic properties of this triangulated category are discussed in [1]. We state the main result, which links the dg-stable category to the orbit category A -grstab /Ω(1).…”
Section: The Dg-stable Categorymentioning
confidence: 99%
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“…We define the differential graded stable category of A to be A -dgstab := D b dg (A)/D perf dg (A). The basic properties of this triangulated category are discussed in [1]. We state the main result, which links the dg-stable category to the orbit category A -grstab /Ω(1).…”
Section: The Dg-stable Categorymentioning
confidence: 99%
“…In this section, we shall study the action of perverse equivalences on a specific triangulated category, namely the dg-stable category of a Brauer tree algebra. The structure of this category was studied in detail in [1], Section 6; we shall work in the same setting and use the same notational conventions, which we summarize below.…”
Section: A Combinatorial Model For a -Dgstabmentioning
confidence: 99%
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