Complex Product Structures on Lie Algebras
Differential Geometry
2007-05-23 v1
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.
Cite
@article{arxiv.math/0305102,
title = {Complex Product Structures on Lie Algebras},
author = {Adrian Andrada and Simon Salamon},
journal= {arXiv preprint arXiv:math/0305102},
year = {2007}
}