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On the Relation of Real and Complex Lie Supergroups

  Published:2015-03-02
 Printed: Jun 2015
  • Matthias Kalus,
    Fakultät für Mathematik , Ruhr-Universität Bochum , Universitätsstraße 150 , D-44801 Bochum, Germany
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Abstract

A complex Lie supergroup can be described as a real Lie supergroup with integrable almost complex structure. The necessary and sufficient conditions on an almost complex structure on a real Lie supergroup for defining a complex Lie supergroup are deduced. The classification of real Lie supergroups with such almost complex structures yields a new approach to the known classification of complex Lie supergroups by complex Harish-Chandra superpairs. A universal complexification of a real Lie supergroup is constructed.
Keywords: Lie supergroup, almost complex structure, Harish-Chandra pair, universal complexification Lie supergroup, almost complex structure, Harish-Chandra pair, universal complexification
MSC Classifications: 32C11, 58A50 show english descriptions Complex supergeometry [See also 14A22, 14M30, 58A50]
Supermanifolds and graded manifolds [See also 14A22, 32C11]
32C11 - Complex supergeometry [See also 14A22, 14M30, 58A50]
58A50 - Supermanifolds and graded manifolds [See also 14A22, 32C11]
 

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