The projective Leavitt complex

2016/10/01 by Huanhuan Li, Li, Huanhuan · 1 citation
Mathematics · #16E45 #16G20 #18E30 #18G35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT #msc:16E45 #msc:16G20 #msc:18E30 #msc:18G35

paper · pdf · doi:10.48550/arxiv.1610.00144

18 pages. arXiv admin note: substantial text overlap with arXiv:1512.04178

openalex publication_date 2016/10/01 · arxiv created 2016/10/10 · arxiv updated 2016/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Q be a finite quiver without sources, and A be the corresponding algebra with radical square zero. We construct an explicit compact generator for the homotopy category of acyclic complexes of projective A-modules. We call such a generator the projective Leavitt complex of Q. This terminology is justified by the following result: the opposite differential graded endomorphism algebra of the projective Leavitt complex of Q is quasi-isomorphic to the Leavitt path algebra of Q ^op. Here, Q^op is the opposite quiver of Q and the Leavitt path algebra of Q^op is naturally Z-graded and viewed as a differential graded algebra with trivial differential.

Citations

• The injective Leavitt complex

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• The injective and projective Leavitt complexes

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