Casper Oelen - Automorphic Lie algebras on complex tori

An automorphic Lie algebra is a Lie algebra of certain invariants which originated in the theory of integrable systems, in the context of reduction of Lax pairs, but then developed as algebraic objects in their own right. They are defined as follows: let a finite group G act on a compact Riemann surface and on a complex finite dimensional Lie algebra, both by automorphisms. Consider the space of meromorphic maps from the Riemann surface to the Lie algebra with poles restricted to a finite set. The subspace of G-equivariant maps is an automorphic Lie algebra. It is an infinite dimensional Lie algebra over the complex numbers and it can be seen as a generalisation of the Onsager algebra. In this talk, I will present automorphic Lie algebras on complex tori where the complex finite dimensional Lie algebra is the special linear Lie algebra of order 2 over the complex numbers.

This event will take place on MS Teams and will be broadcast live in SCH.1.05.