Geodesic
Matrix Lie Groups as 4-Dimensional Hypercomplex Manifolds with Hermitian-Norden Metrics
Journal of Lie theory, Tome 30 (2020) no. 3, pp. 617-626
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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.
Classification : 22E60, 22E15, 53C15, 53C50, 22E30, 53C55
Mots-clés : Lie group, Lie algebra, Matrix representation, Almost hypercomplex structure, Hermitian metric, Norden metric 
@article{JLT_2020_30_3_JLT_2020_30_3_a0,
     author = {H. Manev},
     title = {Matrix {Lie} {Groups} as {4-Dimensional} {Hypercomplex} {Manifolds} with {Hermitian-Norden} {Metrics}},
     journal = {Journal of Lie theory},
     pages = {617--626},
     year = {2020},
     volume = {30},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2020_30_3_JLT_2020_30_3_a0/}
}
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H. Manev. Matrix Lie Groups as 4-Dimensional Hypercomplex Manifolds with Hermitian-Norden Metrics. Journal of Lie theory, Tome 30 (2020) no. 3, pp. 617-626. http://geodesic.mathdoc.fr/item/JLT_2020_30_3_JLT_2020_30_3_a0/