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Algebra Seminar
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Alex Molev
University of Sydney

Casimir elements for some graded Lie algebras and superalgebras

Friday 7th May, 12:05-12:55pm, 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 one-dimensional. 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.