Tuesday, November 23, 2021
Zhengfang Wang, Singularity categories via dg Leavitt path algebras.
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.