Algebra seminar: The cohomological variety of a vertex operator algebra

Participate on site or via Zoom link (meeting ID: 64555726999, for passcode: please contact the organizer)

Abstract: The representation theory of vertex operator algebras (VOA) has been an active field of research for a few decades. During that time, several objects have been defined in order to facilitate the study of VOAs, like the C2 algebra and the Zhu algebra. The goal of this talk is to introduce a new object associated to the cohomology of the C2 algebra of a VOA, namely the cohomological variety. First, we will motivate and define this variety, as well as give some of its structural properties. Then we will explain how to extract information on the Yoneda algebra defining this variety. Lastly, we will apply those results to the Virasoro VOA and the affine VOA associated to a simple Lie algebra. This is a joint work with Cuipo Jiang (Shanghai Jiao Tong University) and Zongzhu Lin (Kansas State University).

This is a seminar in our algebra seminar series.