The singularity category of a Nakayama algebra

2014/04/09 by Dawei Shen, Shen, Dawei · 1 citation
Mathematics · #18E30 #FOS: Mathematics #Primary 16G10 #Representation Theory (math.RT) #Secondary 16D90 #math.RT #msc:16D90 #msc:16G10 #msc:18E30

paper · pdf · doi:10.48550/arxiv.1404.2451

12 pages

arxiv created 2014/04/09 · arxiv updated 2014/04/10

Abstract

Let A be a Nakayama algebra. We give a description of the singularity category of A inside its stable module category. We prove that there is a duality between the singularity category of A and the singularity category of its opposite algebra. As a consequence, the resolution quiver of A and the resolution quiver of its opposite algebra have the same number of cycles and the same number of cyclic vertices.

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• On syzygy categories over Iwanaga-Gorenstein algebras: Reduction, minimality and finiteness

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