Support varieties and representations of tame basic classical Lie superalgebras

Details Support varieties and representations of tame basic classical Lie superalgebras Support varieties and representations of tame basic classical Lie superalgebras

2011-09-13

arxiv.org/abs/1109.2770v1

Mathematics

K-Theory and Homology

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Scientific paper

Let k be an algebraically closed field of characteristic p> 0. For a basic classical Lie superalgebra, we show its restricted cohomology algebra is a finitely generated algebra. Thus the cohomological support theory can be established. As a consequence, we show that the restricted enveloping algebra of a basic classical Lie superalgebra g is always wild except g=sl(2) or g=osp(1|2) or g=C(2). Moreover, all finite dimensional indecomposable restricted representations of u(osp(1|2)), the restricted enveloping algebra of Lie superalgebra osp(1|2), are determined.

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