Complex Product Structures on Lie Algebras

Abstract

A study is made of real Lie algebras admitting compatible complex and product structures, including numerous 4-dimensional examples. If g is a Lie algebra with such a structure then its complexification has a hypercomplex structure. It is shown in addition that g splits into the sum of two left-symmetric subalgebras. Interpretations of these results are obtained that are relevant to the theory of both hypercomplex and hypersymplectic manifolds and their associated connections.

References in corpus (1)

• Abelian complex structures on solvable Lie algebras

Cited by in corpus (6)

• Double products and hypersymplectic structures on $R^{4n}$
• Pseudo-hyperkahler Geometry and Generalized Kahler Geometry
• Geometry of Paraquaternionic Kahler manifolds with torsion
• Metric geometries over the split quaternions
• Hypersymplectic four-dimensional Lie algebras
• Product structures on four dimensional solvable Lie algebras