Tuesday, November 23, 2021

Zhengfang Wang, Singularity categories via dg Leavitt path algebras.

Abstract:
We show that the singularity category of any finite dimensional algebra (given by a quiver with relations) is triangle equivalent to the perfect derived category of a dg Leavitt path algebra. This generalises the well-known result by Chen-Yang and Smith for radical-square-zero algebras. The proof relies on a new dg enhancement of singularity categoy, which we call the singular Yoneda category. We will also provide a deformation-theoretic perspective of this result. This is based on a joint work with X.-W. Chen.