# 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.
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