Speaker: Gao Yun, York University, Canada
Title: P(N)-graded Lie super algebras
Abstract. We generalize the P(N)-graded Lie super algebras of Martinez- Zelmanov. This generalization is not so restrictive but sufficient enough so that we are able to have a classification for this generalized P(N)-graded Lie super-algebras. The upshot is that the generalized P(N)-graded Lie super-algebra L is centrally isogenous to a matrix Lie super-algebra coordinated by an associative super-algebra with a super- involution. Moreover, L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial. This recovers Martinez-Zelmanov’s theorem for type P(N). The motivation of this generalization comes from the fermionic-bosonic module construction.