Non-associative algebras from affine vertex operator algebras

Abstract: Although the definition of a vertex operator algebra (VOA) looks complicated, it's easy to construct non-associative algebras from them. However, this research started somewhere else, with a non-associative algebra constructed explicitly on the 3876-dimensional representation of E8 by Maurice Chayet and Skip Garibaldi. During this talk I will explain the serries of two papers with Tom De Medts and Jari Desmet. In the first paper we show how these algebras can be related to those easy-to-construct non-associative algebras from VOAs. In the second paper we explain how this vertex algebra structure provides insights in this 3876-dimensional algebra by computing the fusion rules for certain idempotents.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar