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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Atypicality, complexity and module varieties for classical Lie superalgebras

## Atypicality, complexity and module varieties for classical Lie superalgebrasAdd to your list(s) Download to your calendar using vCal - Nakano, D (Georgia)
- Tuesday 23 June 2009, 14:00-15:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Algebraic Lie Theory Let ${mathfrak g}={mathfrak g} In this talk we investigate the homological properties of the category ${mathcal F}$. In particular we prove that ${mathcal F}$ is self-injective in the sense that all projective supermodules are injective. We also show that all supermodules in ${mathcal F}$ admit a projective resolution with polynomial rate of growth and, hence, one can study complexity in $mathcal{F}$. If ${mathfrak g}$ 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. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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