Results 221 to 230 of about 541 (254)

Reduction of Representations of the General Linear Group Using Lie Algebras

SIAM Journal on Applied Mathematics, 1973
By considering the Lie algebra of the general linear group in ndimensions over the complex field $GL( {n,\mathbb{C}} )$ and inspecting the weight diagrams corresponding to its irreducible representations it may be possible to see how a representation of $GL( {n,\mathbb{C}} )$ reduces into irreducible representations of a subgroup.
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Construction of invariants of the coadjoint representation of Lie groups using linear algebra methods

Theoretical and Mathematical Physics, 2016
After the works of Casimir in 1931, invariant functions of the coadjoint representation were called \textit{Casimir functions}. The study of such invariants is important because of many applications in mathematics and physics. The problem of constructing these representations for semisimple Lie algebras is already solved, although such a problem for ...
Kurnyavko, O. L., Shirokov, I. V.
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SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems. II. Realizations of the Lie algebra

Journal of Mathematical Physics, 1988
The two-dimensional space-time realizations of the Lie algebra of SL(3,R) are obtained, when the group acts as the maximal point symmetry group of any given one-dimensional Newtonian linear system. It is shown that these realizations are isomorphic with the realization of the Lie algebra of the projective group in the plane.
Aguirre, M., Krause, J.
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A free Lie algebra as a module over the full linear group

Sbornik: Mathematics, 1996
Let \(L=L(x_1,\ldots,x_m)\) be the free Lie algebra of finite rank \(m>1\) over a field \(F\) of characteristic 0. The general linear group \(GL_m(F)\) acts naturally on \(L\). The main problem discussed in the paper under review is to evaluate the multiplicities \(m_{\lambda}\) of the irreducible polynomial \(GL_m(F)\)-modules participating in the ...
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General Hypergeometric Functions of Matrices and their Connection to Representations of Linear Groups and Lie Algebras

Acta Applicandae Mathematicae, 2005
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Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures

American Journal of Mathematics, 1990
Introduction. Let L be a finite dimensional Lie algebra over the real numbers, R, and let L* be its dual vector space. It is well-known [24] that the Lie algebra structure on L defines a natural Poisson structure on L*-in fact this was already known to Lie [24]-and these Poisson structures are exactly what are now called the linear Poisson structures ...
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Linear representations of the Lie algebra of the diffeomorphism group in $$\mathbb{R}^d$$

Theoretical and Mathematical Physics
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2-Generation of simple Lie algebras and free dense subgroups of algebraic groups

Journal of Algebra, 2020
Willem A De Graaf
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On Certain Algebraic Structures Associated with Lie (Super)Algebras

Springer Proceedings in Mathematics and Statistics, 2023
Noriaki Kamiya
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Linear Bundle of Lie Algebras Applied to the Classification of Real Lie Algebras

Symmetry, 2021
Alina Dobrogowska, Dobrogowska Alina
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