Lie Supergroups: An operator viewpoint

Details Lie Supergroups: An operator viewpoint Lie Supergroups: An operator viewpoint

2010-12-20

arxiv.org/abs/1012.4456v1

Mathematics

Rings and Algebras

Scientific paper

Representation-theoretical Lie supergroups are introduced as supermanifolds with underlying base manifold being the Lie group associated to the even part of a given Lie superalgebra. The Lie superalgebra is required to be represented by invariant derivations on the space of superfunctions. This approach does not involve the morphisms for multiplication, inverse and identity as in the category-theoretical approach to Lie supergroups. The constructed category is not isomorphic to the category of Harish-Chandra superpairs. Variation of structure occurs. First examples where positive-dimensional parameter spaces arise are computed.

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