In this talk we will discuss ongoing work to use relative cohomology to study the representation theory of Lie superalgebras over the complex numbers. In particular, one sees that the cohomology ring is finitely generated (in fact, a polynomial ring), and one is naturally led to the theory of support varieties for Lie superalgebras. Our investigations have shown that this approach has close connections to both the representation theory and combinatorics of Lie superalgebras. In particular, we will discuss our efforts to calculate specific examples and to extend the theory to the Cartan-type simple Lie superalgebras. This work is joint with Brian Boe, Daniel Nakano, and Irfan Bagci.

Lecture #12716

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