CENTERS OF CLASSICAL LIE SUPERALGEBRAS
by Maria GORELIK (Weizmann Institute of Science, Israel)
Abstract:
The center of the enveloping algebra of a semi-simple Lie algebra
was described in classical works of Chevalley and Harish-Chandra.
If g=gl(n) then the center is canonically isomorphic to the
algebra of symmetric polynomials of n variables.
For an arbitrary semi-simple Lie algebra the center of the universal
enveloping algebra is a polynomial algebra.
The situation is quite different for Lie superalgebras:
even for gl(m|n), the most straightforward analogue of gl(n),
the center is not polynomial and even is not finitely generated.
In this talk we will explain different approaches to a description
of the center of the enveloping algebra of simple Lie superalgebras.
Also we will discuss the notion of the anticenter for Lie superalgebras.
I will review different approaches to a description of
centres of the enveloping algebra of a classical Lie superalgebra.