Left invariant complex structures on U(2) and SU(2)xSU(2) revisited

Details Left invariant complex structures on U(2) and SU(2)xSU(2) revisited Left invariant complex structures on U(2) and SU(2)xSU(2) revisited

2008-09-06

arxiv.org/abs/0809.1182v2

Mathematics

Rings and Algebras

25 pages. v2: A very important reference has been added. Correspondingly, slight changes in the introduction, and an added Rem

Scientific paper

We compute the torsion-free linear maps from the Lie algebra su(2) into itself, deduce a new determination of the integrable complex structures and their equivalence classes under the action of the automorphism group for u(2) and su(2)xsu(2), and prove that in both cases the set of complex structures is a differentiable manifold. u(2)x u(2), su(2)^N and u(2)^N are also considered. Extensions of complex structures from u(2) to su(2)xsu(2) are studied, local holomorphic charts given, and attention is paid to what representations of u(2) we can get from a substitute to the regular representation on a space of holomorphic functions for the complex structure.

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