On the Relation of Real and Complex Lie Supergroups
Printed: Jun 2015
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
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
Lie supergroup, almost complex structure, Harish-Chandra pair, universal complexification
32C11 - Complex supergeometry [See also 14A22, 14M30, 58A50]
58A50 - Supermanifolds and graded manifolds [See also 14A22, 32C11]