caa a22 4500 445862211 CHVBK 20180317145447.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00031-010-9114-5 doi (NATIONALLICENCE)springer-10.1007/s00031-010-9114-5 Vishnyakova E. Department of Mathematics, Ruhr-Universität Bochum, D-44801, Bochum, Germany aut On complex lie supergroups and split homogeneous supermanifolds [Elektronische Daten] [E. Vishnyakova] It is well known that the category of real Lie supergroups is equivalent to the category of the so-called (real) Harish-Chandra pairs, see [DM], [Kost], [Kosz]. That means that a Lie supergroup depends only on the underlying Lie group and its Lie superalgebra with certain compatibility conditions. More precisely, the structure sheaf of a Lie supergroup and the supergroup morphisms can be explicitly described in terms of the corresponding Lie superalgebra. In this paper we give a proof of this result in the complex-analytic case. Furthermore, if (G, $$ \mathcal{O} $$ G) is a complex Lie supergroup and H ⊂ G is a closed Lie subgroup, i.e., it is a Lie subsupergroup of (G, $$ \mathcal{O} $$ G) and its odd dimension is zero, we show that the corresponding homogeneous supermanifold (G/H, $$ \mathcal{O} $$ G/H) is split. In particular, any complex Lie supergroup is a split supermanifold. It is well known that a complex homogeneous supermanifold may be nonsplit (see, e.g., [OS1]). We find here necessary and sufficient conditions for a complex homogeneous supermanifold to be split. Springer Science+Business Media, LLC, 2010 Transformation Groups SP Birkhäuser Verlag Boston 16/1(2011-03-01), 265-285 1083-4362 16:1<265 2011 16 31 https://doi.org/10.1007/s00031-010-9114-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-010-9114-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Vishnyakova E. Department of Mathematics, Ruhr-Universität Bochum, D-44801, Bochum, Germany aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/1(2011-03-01), 265-285 1083-4362 16:1<265 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer