This week's seminars
Geometry and Topology Seminar: The Wildness and Local Structure of Automorphic Lie Algebras
14 November 2019 13:00 in CM301
Automorphic Lie algebras are a class of infinite-dimensional Lie algebras that are closely related to a wide variety of algebraic structures that appear in integrable systems theory, mathematical physics and geometry. They can be viewed as a certain generalisation of the well-studied (twisted) loop algebras and current algebras. It can often be difficult to immediately gain an intuitive understanding of the algebraic structure behind an automorphic Lie algebra. However, this task can be made easier using techniques in representation theory. Associated to an automorphic Lie algebra is a commutative algebra of functions. Studying automorphic Lie algebras via evaluation maps parameterised by the representations of the associated commutative algebra provides a descending chain of ideals of the automorphic Lie algebra. A detailed study of this chain of ideals immediately shows that the representation theory of automorphic Lie algebras is wild, and enables us to describe the local Lie structure of the automorphic Lie algebra.