Emmy-Noether-Seminar: Universal 2-parameter algebras in VOA theory

Universal 2-parameter algebras in VOA theory

Vladimir Kovalchuk

Abstract: Vertex algebras are a non-commutative and non-associative generalization of differential algebras. Of these, W-algebras form an important family of finitely (strongly) generated algebras, defined over (a localization) of a polynomial ring in 1 variable. These can be organized into families, based on their (strong) generating type pattern. Such families can be uniformly studied from the perspective of so-called universal 2-parameter algebras; they are infinitely (strongly) generated according to a nice pattern, and defined over a polynomial ring in 2 variables. We explain why these are nice, and if time permits, the idea behind their construction.