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Invariant generalized complex structures on Lie groups. (English) Zbl 1264.53035

The authors describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group \(G\). In the case when \(G\) is a semisimple Lie group of inner type (in particular, when \(G\) is compact semisimple), a classification of regular generalized complex structures on \(G\) is given. They show that any invariant generalized complex structure on a compact semisimple Lie group is regular, provided that an additional natural condition is satisfied.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C30 Differential geometry of homogeneous manifolds
53C80 Applications of global differential geometry to the sciences
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