Cohomology and Support Varieties for Lie Superalgebras

Details Cohomology and Support Varieties for Lie Superalgebras Cohomology and Support Varieties for Lie Superalgebras

2006-09-13

arxiv.org/abs/math/0609363v1

Mathematics

Representation Theory

Submitted

Scientific paper

We study cohomology for classical Lie superalgebras $\mathfrak{g}$ (e.g. gl(m|n)) over the complex numbers. Using results from invariant theory, we show that there exist subsuperalgebras which detect the cohomology of $\mathfrak{g}.$ Furthermore, drawing inspiration from finite groups and restricted Lie algebras, we introduce the notion of support varieties in this context. One can prove these varieties have many of the desirable properties of such a theory. They also appear to provide new interpretations for certain combinatorics associated with Lie superalgebras.

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