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Adrián Andrada, Simon Salamon

Complex product structures on Lie algebras

A study is made of real Lie algebras admitting compatible complex and product structures, including numerous 4-dimensional examples. Any Lie algebra ? with such a structure is even-dimensional and its complexification has a hypercomplex structure. In addition, ? splits into the direct sum of two Lie subalgebras of the same dimension, and each of these is shown to have a left-symmetric algebra (LSA) structure. Interpretations of these results are obtained that are relevant to the theory of both hypercomplex and hypersymplectic manifolds and their associated connections.

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 17, 03/2005
Pages: 261 - 295

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