
Alex Molev
University of Sydney
Casimir elements for some graded Lie algebras and superalgebras
Friday 7th May, 12:0512:55pm,
Carslaw 373.
We consider a class of Lie algebras L such that L admits a
grading by
a finite abelian group so that each nontrivial homogeneous component
is onedimensional. In particular, this class contains simple Lie
algebras of type A, C or D where in C and D cases the rank of L is a
power of 2. We give a simple construction of a family of central
elements of the universal enveloping algebra U(L). We show that for
the A type Lie algebras the elements coincide with the Gelfand
invariants and thus generate the center of U(L). The construction can
be extended to Lie superalgebras with the additional assumption that
the group grading is compatible with the parity grading.
This is joint work with Yuri Bahturin.







