Finite Weight Modules over Affine Lie Superalgebras

Abstract: Nonzero real vectors of an affine Lie superalgebra act on a simple module either locally nilpotently or injectively. This helps us to divide simple finite weight modules over a twisted affine Lie superalgebra $\mathfrak{L}$ into two subclasses called hybrid and tight. We will talk about the characterization as well as the classification problem of modules in each subclass. In this regard, the classification of bases of the root system of $\mathfrak{L}$ is crucial. We will discuss how we can classify the bases and how we can use the obtained classification to study simple finite weight modules over $\mathfrak{L}.$

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar