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The Projective Leavitt Complex
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 61 / Issue 4 / November 2018
- Published online by Cambridge University Press:
- 15 August 2018, pp. 1155-1177
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- Article
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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.
