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Homotopy Categories, Leavitt Path Algebras, and Gorenstein Projective Modules.
- Source :
-
IMRN: International Mathematics Research Notices . 2015, Vol. 2015 Issue 10, p2597-2633. 37p. - Publication Year :
- 2015
-
Abstract
- For a finite quiver without sources or sinks, we prove that the homotopy category of acyclic complexes of injective modules over the corresponding finite-dimensional algebra with radical square zero is triangle equivalent to the derived category of the Leavitt path algebra viewed as a differential graded algebra with trivial differential, which is further triangle equivalent to the stable category of Gorenstein projective modules over the trivial extension algebra of a von Neumann regular algebra by an invertible bimodule. A related, but different, result for the homotopy category of acyclic complexes of projective modules is given. Restricting these equivalences to compact objects, we obtain various descriptions of the singularity category of a finite-dimensional algebra with radical square zero, which contain previous results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10737928
- Volume :
- 2015
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- IMRN: International Mathematics Research Notices
- Publication Type :
- Academic Journal
- Accession number :
- 102934859
- Full Text :
- https://doi.org/10.1093/imrn/rnu008