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Infinitely divisible projective representations of the Lie algebras

Mathematical Proceedings of the Cambridge Philosophical Society, 1972
Infinitely divisible group representations were first defined by Streater(1) as an important concept closely related to continuous tensor product. Araki(2) analysed the factorizable representations of Lie groups and obtained a generalization of the Levy–Khinchine formula.
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Description of a class of projection operators for semisimple complex Lie algebras

Mathematical Notes of the Academy of Sciences of the USSR, 1979
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Asherova, R. M.   +2 more
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Fundamental theorem of projective geometry in Lie modules and algebras

Journal of Soviet Mathematics, 1988
Es ist wohlbekannt, daß jeder Automorphismus eines projektiven Raumes über einem Schiefkörper K (oder des zugehörigen Unterraumverbandes) durch eine semilineare Abbildung des zugehörigen K-Vektorraumes X induziert werden kann (Hauptsatz der projektiven Geometrie). Verf.
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Lie algebras of infinitesimal projective transformations of Lorentz manifolds

Russian Mathematical Surveys, 1995
This article includes four chapters: Infinitesimal projective transformations; Affine and projective transformations determinated by circular vector fields; Lorentz manifolds and affine and projective transformations; The classification of Lorentz manifolds in Lie algebras of infinitesimal projective transformations.
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Lie algebras of projective motions of h-spaces H32,2 of type {32}

Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
We study 5-dimensional pseudo-Riemannian manifolds in the form of h-spaces H 32 of type {32}. A classification of h-spaces H 32 ,
A. V. Aminova, D. R. Khakimov
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Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. IV. Structure of projective and affine Lie algebras of five-dimensional rigid $h$-spaces

Итоги науки и техники Серия «Современная математика и ее приложения Тематические обзоры», 2022
Asya Vasilyevna Aminova   +1 more
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Lie algebras of projective motions of five-dimensional pseudo-Riemannian spaces. V. Lie algebras of projective and affine motions of $h$-spaces $H_{221}$ of type $\{221\}$

Итоги науки и техники Серия «Современная математика и ее приложения Тематические обзоры», 2022
Asya Vasilyevna Aminova   +1 more
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Direct Integral Decomposition of Two-Projection Algebras and Fiberwise Lie Algebra Structure of su(2)

We study the von Neumann algebra \mathcal{M} = \{P,Q\}'' generated by two orthogonal projections on a separable Hilbert space. Using the Halmos direct integral decomposition in the sense of Dixmier and Takesaki, we show that \mathcal{M} decomposes into abelian parts and a measurable field of copies of M_2(\mathbb{C}).
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