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On the Relation of Real and Complex Lie Supergroups

Published online by Cambridge University Press:  20 November 2018

Matthias Kalus
Matthias Kalus*
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraβe 150, D- 44801 Bochum, Germany. e-mail: matthias.kalus@rub.de
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Abstract

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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 complexHarish-Chandra superpairs. A universal complexification of a real Lie supergroup is constructed.

Keywords

32C1158A50Lie supergroupalmost complex structureHarish–Chandra pairuniversal complexification
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 2 , 01 June 2015 , pp. 281 - 284
Copyright
Copyright © Canadian Mathematical Society 2015

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