Research Seminar in Mathematics - Lie algebras of vector fields and their representations

Speaker

Jonathan Nilsson, Örebro University.

Abstact

Lie groups and Lie algebras describe sets of symmetries, which is why they appear so frequently throughout mathematics and physics. The finite dimensional simple Lie algebras and their representations were extensively studied by Sophus Lie and Élie Cartan in the 19th and early 20th century. In particular, all finite dimensional representations were classified. By contrast, much less is known about infinite dimensional Lie algebras. A classical type of infinite dimensional Lie algebras comes from the field of geometry: If X is an algebraic variety (such as a sphere or a torus for example) we can study the set of vector fields on X - these form a Lie algebra in a natural way. In this talk I will discuss this type of Lie algebras and their representations from an algebraic point of view. The talk is based on joint work with Y. Billig and V. Futorny.