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Journal of Lie Theory 30 (2020), No. 3, 617--626
Copyright Heldermann Verlag 2020

Matrix Lie Groups as 4-Dimensional Hypercomplex Manifolds with Hermitian-Norden Metrics

Hristo Manev
Department of Medical Informatics, Faculty of Public Health, Medical University Plovdiv, Plovdiv 4002, Bulgaria

There are studied Lie groups considered as almost hypercomplex Hermitian-Norden manifolds, which are integrable and have the lowest dimension four. It is established a correspondence of the derived types Lie algebras with invariant hypercomplex structures and the explicit matrix representation of their Lie groups. There are constructed examples of the considered structure of different types on some known Lie groups.

Keywords: Lie group, Lie algebra, Matrix representation, Almost hypercomplex structure, Hermitian metric, Norden metric.

MSC: 22E60, 22E15, 53C15, 53C50, 22E30, 53C55.

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