An invariant supertrace for the category of representations of Lie superalgebras

Details An invariant supertrace for the category of representations of Lie superalgebras An invariant supertrace for the category of representations of Lie superalgebras

2007-11-27

arxiv.org/abs/0711.4231v1

Mathematics

Representation Theory

19 pages

Scientific paper

In this paper we give a re-normalization of the supertrace on the category of representations of Lie superalgebras of type I, by a kind of modified superdimension. The genuine superdimensions and supertraces are generically zero. However, these modified superdimensions are non-zero and lead to a kind of supertrace which is non-trivial and invariant. As an application we show that this new supertrace gives rise to a non-zero bilinear form on a space of invariant tensors of a Lie superalgebra of type I. The results of this paper are completely classical results in the theory of Lie superalgebras but surprisingly we can not prove them without using quantum algebra and low-dimensional topology.

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