To participate in this seminar, please register HERE.

What are central extensions of Lie algebras (and groups) and why are they interesting?

We will look at the central extensions applied to the Virasoro algebra using the Gelfand-Fuks cocycle.

Then we will revisit the question of how to find the Lie algebra of Diff(S^1) from last meeting.

We will also discuss how the complexification of the Witt algebra is relevant to these objects.

Some of the difficulties we will mention include the lack of finite-dimensional correspondence between Lie algebras and simply connected Lie groups.