Complex product structures on Lie algebras

ADRIÁN ANDRADA; SIMON SALAMON

FORUM MATHEMATICUM

WALTER DE GRUYTER & CO

Lugar: Berlin; Año: 2005 vol. 17 p. 261 - 295

0933-7741

A study is made of real Lie algebras admitting compatible complex and product structures, including numerous 4-dimensional examples. Any Lie algebra g with such a structure is even-dimensional and its complexification has a hypercomplex structure. In addition, g 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.