Journal of Lie Theory

no. 3
Matrix Lie Groups as 4-Dimensional Hypercomplex Manifolds with Hermitian-Norden Metrics
Journal of Lie Theory, Volume 30 (2020) no. 3, pp. 617-626
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.
DOI: 10.5802/jolt.1131
Classification: 22E60, 22E15, 53C15, 53C50, 22E30, 53C55
Keywords: Lie group, Lie algebra, Matrix representation, Almost hypercomplex structure, Hermitian metric, Norden metric 
@article{JOLT_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},
     doi = {10.5802/jolt.1131},
     zbl = {1479.22018},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1131/}
}
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H. Manev. Matrix Lie Groups as 4-Dimensional Hypercomplex Manifolds with Hermitian-Norden Metrics. Journal of Lie Theory, Volume 30 (2020) no. 3, pp. 617-626. doi: 10.5802/jolt.1131

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