University of Sydney Algebra Seminar

Masoud Kamgarpour (University of Queensland)

Friday 7th June, 12:05-12:55pm, Carslaw 373

On the center of Lie algebras

I will discuss the center of (the universal enveloping algebra) four different kinds of Lie algebras:

1. Harish-Chandra's description of the centre of a simple algebra \(\mathfrak{g}\);
2. Kirillov-Duflo's description of the centre of an arbitrary finite dimensional algebra;
3. Center of the jet algebra \(\mathfrak{g}[[t]]\) and loop algebra \(\mathfrak{g}((t))\);
4. Feigin-Frenkel description of center of the vertex Lie algebra associated to \(\mathfrak{g}\).

I will then define the notion of quasi-Verma modules for the above mentioned vertex algebra, and stipulate how the Feigin-Frenkel Center should act on these modules.