# University of Toronto's Symplectic Geometry Seminar

October 2, 2006, 3:10pm

SS 2128

## Emanuela Petracci

### University of Toronto

## a formula for Gorelik's invariant

**Abstract: **Abstract:
In the '90, physicists introduced a notion of "Casimir's ghost"
for a Lie superalgebra $g$. It is a special element of the envelopping
algebra of $g$ and it is invariant for a certain action of $g$. In 2000,
M. Gorelik showed that such an element $T$ exists if $g$ is
finite-dimensional and unimodular. Later, she also explained why this
element is important in Representation Theory of Lie superalgebras.
In this talk we present an explicit formula of $T$ and a method to get
it. We also explain what happens when we remove the unimodularity
hypothesis. This formula is related to the Jacobian of the exponential
map.