The singularity category of a quadratic monomial algebra*

Abstract

We exploit singular equivalences between artin algebras that are induced from certain functors between the stable module categories. Such functors are called pre-triangle equivalences. We construct two pre-triangle equivalences connecting the stable module category over a quadratic monomial algebra to the one over an algebra with radical square zero. Consequently, we obtain an explicit singular equivalence between the two algebras. It turns out that this singular equivalence restricts to a triangle equivalence between their stable categories of Gorenstein-projective modules, and thus induces a triangle equivalence between their Gorenstein defect categories.

Locations

• arXiv (Cornell University) - View - PDF
• The Quarterly Journal of Mathematics - View