Atypicality, complexity and module varieties for classical Lie superalgebras

Add 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.

This talk has been canceled/deleted

Let ${mathfrak g}={mathfrak g}oplus {mathfrak g}{
}$ be a classical Lie superalgebra and ${mathcal F}$ be the category of finite dimensional ${mathfrak g}$-supermodules which are semisimple over ${mathfrak g}_{}$.

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:

This talk is not included in any other list

Note that ex-directory lists are not shown.