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

N. Blazic; S. Vukmirovic

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

N. Blazic·S. Vukmirovic

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Abstract

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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N. Blazic, S. Vukmirovic. 2003-10-13. Classification of four-dimensional Lie algebras admitting a para-hypercomplex structure. https://arxiv.org/abs/math/0310180

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