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arXiv · 0905.2403

Complexity and module varieties for classical Lie superalgebras

Brian D. Boe·Jonathan R. Kujawa·Daniel K. Nakano
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Abstract

Let g=g_{0} \oplus g_{1} be a classical Lie superalgebra and F be the category of finite dimensional g-supermodules which are semisimple over g_{0}. In this paper we investigate the homological properties of the category F. In particular we prove that F is self-injective in the sense that all projective supermodules are injective. We also show that all supermodules in F admit a projective resolution with polynomial rate of growth and, hence, one can study complexity in F. If g is a Type I Lie superalgebra we introduce support varieties which detect projectivity and are related to the associated varieties of Duflo and Serganova. If in addition g has a (strong) duality then we prove that the conditions of being tilting or projective are equivalent.

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BibTeXRIS

Brian D. Boe, Jonathan R. Kujawa, Daniel K. Nakano. 2009-05-14. Complexity and module varieties for classical Lie superalgebras. https://arxiv.org/abs/0905.2403

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