The graded centers of derived discrete algebras

2009/06/08 by Grzegorz Bobiński, Grzegorz Bobinski, Bobinski, Grzegorz
Mathematics · #16G20 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT #msc:16G20 #msc:18E30

paper · pdf · doi:10.48550/arxiv.0906.1567

arxiv created 2009/06/08 · openalex publication_date 2009/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe in the paper the graded centers of the derived categories of the derived discrete algebras. In particular, we prove that if A is a derived discrete algebra, then the reduced part of the graded center of the derived category of A is nontrivial if and only if A has infinite global dimension. Moreover, we show that the nilpotent part of the graded center is controlled by the objects for which the Auslander--Reiten translation coincides with a power of the suspension functor.

Citations

• The almost split triangles for perfect complexes over gentle algebras

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