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.