
Journal of Lie Theory 30 (2020), No. 3, 617626 Copyright Heldermann Verlag 2020 Matrix Lie Groups as 4Dimensional Hypercomplex Manifolds with HermitianNorden Metrics Hristo Manev Department of Medical Informatics, Faculty of Public Health, Medical University Plovdiv, Plovdiv 4002, Bulgaria hristo.manev@muplovdiv.bg There are studied Lie groups considered as almost hypercomplex HermitianNorden 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. [ Fulltextpdf (111 KB)] for subscribers only. 