Indecomposable representations of Lie superalgebras

Details Indecomposable representations of Lie superalgebras Indecomposable representations of Lie superalgebras

2002-02-18

arxiv.org/abs/math/0202184v1

In: A. N. Sissakian et. al. (ed.), {\em Memorial volume dedicated to Misha Saveliev and Igor Luzenko}, JINR, Dubna, 2000, 126-

Mathematics

Representation Theory

10 p., Latex

Scientific paper

In 1960's I. Gelfand posed a problem: describe indecomposable representations of any simple infinite dimensional Lie algebra of polynomial vector fields. Here, by applying the elementary technique of Gelfand and Ponomarev, a toy model of the problem is solved: finite dimensional indecomposable representations of vect(0|2), the Lie superalgebra of vector fields on the (0|2)-dimensional superspace, are described. Since vect (0|2) is isomorphic to sl(1|2) and osp(2|2), their representations are also described. The result is generalized in two directions: for sl(1|n) and osp(2|2n). Independently and differently J. Germoni described indecomposable representation of the series sl(1|n) and several individual Lie superalgebras. Partial results for other simple Lie superalgebras without Cartan matrix are reviewed. In particular, it is only for vect(0|2) and sh(0|4) that the typical irreducible representations can not participate in indecomposable modules; for other simple Lie superalgebras without Cartan matrix (of series vect(0|n), svect(0|n)$, svect(0|n)', spe(n) for n>2 and sh(0|m) for m>4) one can construct indecomposable representations with arbitrary composition factors. Several tame open problems are listed, among them a description of odd parameters

Affiliated with

Also associated with

No associations

Rating

Indecomposable representations of 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 Indecomposable representations of Lie superalgebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Indecomposable representations of Lie superalgebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-302840