Complexity and module varieties for classical Lie superalgebras

Details Complexity and module varieties for classical Lie superalgebras Complexity and module varieties for classical Lie superalgebras

2009-05-14

arxiv.org/abs/0905.2403v1

Mathematics

Representation Theory

21 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Complexity and module varieties for classical Lie superalgebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Complexity and module varieties for classical Lie superalgebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complexity and module varieties for classical Lie superalgebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-401416