We introduce a notion of a root groupoid as a replacement of the notion of Weyl group for (Kac-Moody) Lie superalgebras. The objects of the root groupoid classify certain root data, the arrows are defined by generators and relations. As an abstract groupoid the root groupoid has many connected components and we show that to some of them one can associate an interesting family of Lie superalgebras which we call root superalgebras. To each root groupoid component we associate a graph (called skeleton) generalizing the Cayley graph of the Weyl group. The skeleton satisfies a version of Coxeter property generalizing the fact that the Weyl group of a Kac-Moody Lie algebra is Coxeter. This talk in based on a joint work with V. Serganova and M. Gorelik, arXiv:2209.06253.

# Cable Car Algebra Seminar: Root groupoid and Lie superalgebras

Abstract: