Classification of four-dimensional Lie algebras admitting a para-hypercomplex structure

Details Classification of four-dimensional Lie algebras admitting a para-hypercomplex structure Classification of four-dimensional Lie algebras admitting a para-hypercomplex structure

2003-10-13

arxiv.org/abs/math/0310180v1

Mathematics

Differential Geometry

15 pages

Scientific paper

The main goal is to classify 4-dimensional real Lie algebras $\g$ which admit a para-hypercomplex structure. This is a step toward the classification of Lie groups admitting the corresponding left-invariant structure and therefore possessing a neutral, left-invariant, anti-self-dual metric. Our study is related to the work of Barberis who classified real, 4-dimensional simply-connected Lie groups which admit an invariant hypercomplex structure.

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