The Singularity Category of an Algebra with Radical Square Zero

To an artin algebra with radical square zero, a regular algebra in the sense of von Neumann and a family of invertible bimodules over the regular algebra are associated. These data describe completely, as a triangulated category, the singularity category of the artin algebra. A criterion on the Hom-finiteness of the singularity category is given in terms of the valued quiver of the artin algebra.

2010 Mathematics Subject Classification: 18E30, 13E10, 16E50

Keywords and Phrases: singularity category, von Neumann regular algebra, invertible bimodule, valued quiver

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