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SUMMARY:Atypicality\, complexity and module varieties for classical Lie su
 peralgebras - Nakano\, D (Georgia)
DTSTART:20090623T130000Z
DTEND:20090623T140000Z
UID:TALK18870@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Let ${mathfrak g}={mathfrak g}_{}oplus {mathfrak g}_{
}$ be a 
 classical Lie superalgebra and ${mathcal F}$ be the category of finite dim
 ensional ${mathfrak g}$-supermodules which are semisimple over ${mathfrak 
 g}_{}$. \n\nIn 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 resolu
 tion with polynomial rate of growth and\, hence\, one can study complexity
  in $mathcal{F}$. If ${mathfrak g}$ is a Type~I Lie superalgebra we introd
 uce support varieties which detect projectivity and are related to the ass
 ociated varieties of Duflo and Serganova. If in addition $g$ has a (stron
 g) duality then we prove that the conditions of being tilting or projectiv
 e are equivalent. \n\n
LOCATION:Seminar Room 1\, Newton Institute
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