Sub-Lorentz geodesics on GL^{+}(2,C) with the generating space of Hermitian matrices in the Lie algebra gl^{+}(2,C) Full article
| Journal |
Pure and Applied Functional Analysis
ISSN: 2189-3756 , E-ISSN: 2189-3764 |
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| Output data | Year: 2025, Volume: 10, Number: 2, Pages: 211--238 Pages count : 28 | ||||
| Tags | Hermitian matrix, Pauli matrices, Pontryagin minimum principle, Riemannian symmetric space, sub-Lorentzian (ab)normal extremal, sub-Lorentzian geodesic, sub-Lorentzian longest arc, | ||||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
| 2 | Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН». | FWNF-2022-0003 |
Abstract:
The Lie subgroup GL^{+}(2,C) of all matrices in the Lie group GL(2,C) with positive real determinant is equipped with a left-invariant sub-Lorentzian (anti)metric, defined by the natural structure of the 4-dimensional Minkowski space-time on the subspace of Hermitian matrices in its Lie algebra. On base of the corresponding time-anti-optical control problem, formulated in the paper, and Pontryagin minimum principle for it, using geoesics and shortest arcs of the corresponding left-invariant sub-Riemannian metric on the Lie subgroup SL(2,C), the authors found sub-Lorentzian nonspacelike geodesics and longest arcs.
Cite:
Berestovskii V.
, Zubareva I.
Sub-Lorentz geodesics on GL^{+}(2,C) with the generating space of Hermitian matrices in the Lie algebra gl^{+}(2,C)
Pure and Applied Functional Analysis. 2025. V.10. N2. P.211--238.
Sub-Lorentz geodesics on GL^{+}(2,C) with the generating space of Hermitian matrices in the Lie algebra gl^{+}(2,C)
Pure and Applied Functional Analysis. 2025. V.10. N2. P.211--238.
Dates:
| Submitted: | Oct 27, 2023 |
| Accepted: | Jan 24, 2024 |
| Published print: | May 13, 2025 |
| Published online: | May 13, 2025 |
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