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The Projective Leavitt Complex

Part of: Abelian categories Homological algebra Representation theory of rings and algebras Homological methods

Published online by Cambridge University Press:  15 August 2018

Huanhuan Li
Huanhuan Li*
Affiliation:
Centre for Research in Mathematics, Western Sydney University, Sydney, NSW 2150, Australia ([email protected])
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Abstract

For a finite quiver Q without sources, we consider the corresponding radical square zero algebra A. 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 Qop. Here, Qop is the opposite quiver of Q, and the Leavitt path algebra of Qop is naturally ${\open Z}$-graded and viewed as a differential graded algebra with trivial differential.

Keywords

Leavitt path algebraprojective Leavitt complexcompact generatordg quasi-balanced module

MSC classification

Primary: 16G20: Representations of quivers and partially ordered sets
Secondary: 16E45: Differential graded algebras and applications 18E30: Derived categories, triangulated categories 18G35: Chain complexes
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 4 , November 2018 , pp. 1155 - 1177
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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