Left invariant complex structures on U2 and SU2xSU2 revisited - Mathematics > Rings and AlgebrasReport as inadecuate




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Abstract: We compute the torsion-free linear maps from the Lie algebra su2 intoitself, deduce a new determination of the integrable complex structures andtheir equivalence classes under the action of the automorphism group for u2and su2xsu2, and prove that in both cases the set of complex structures isa differentiable manifold. u2x u2, su2^N and u2^N are also considered.Extensions of complex structures from u2 to su2xsu2 are studied, localholomorphic charts given, and attention is paid to what representations of u2we can get from a substitute to the regular representation on a space ofholomorphic functions for the complex structure.



Author: Louis Magnin

Source: https://arxiv.org/







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