On cohomology and support varieties for Lie superalgebras

By I. Bagci. 2010

52 citations recorded by the source corpus.

Let $mathfrak{g}$ be a restricted Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$. Let $\mathfrak{u}(\mathfrak{g})$ denote the restricted enveloping algebra of $\mathfrak{g}$. In this paper we prove that the cohomology ring $\HH^\bullet(\fu(\fg), k)$ is finitely generated. This allows one to define support varieties for finite dimensional $\fu(\fg)$-supermodules. We also show that support varieties for finite dimensional $\fu(\fg)$ supermodules satisfy the desirable properties of support variety theory.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5a396c61a20c9d6de999a672989243b85a44aa47

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In Algebra and Number Theory

1. Jonathan R. Kujawa
2. Nathan Geer
3. Bertrand Patureau-Mirand

In Geometry and Topology

1. Nathan Geer
2. Bertrand Patureau-Mirand
3. Jonathan R. Kujawa
4. Alexis Virelizier

Citations in the corpus

• Generalized trace and modified dimension functions on ribbon categories (2010, methodology): “[ 13 ,19,34]), and recently Serganova has announced a proof for the classical contragradiant Lie superalgebras using category equivalences, Zuckerman functors, and a character formula of Penkov [51].”