Results 181 to 190 of about 54,650 (190)

An interesting representation of lie algebras of linear groups

International Journal of Theoretical Physics, 1976
I have presented a means of getting a representation space of a general linear group ofn dimensions in terms of homogeneous functions ofn,n-dimensional vectors. Except in particular cases, the representation is of the Lie algebra, rather than the group.
openaire   +2 more sources

Linear Algebraic Groups and Finite Groups of Lie Type

2011
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups.
Gunter Malle, Donna Testerman
openaire   +1 more source

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.
openaire   +1 more source

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.
openaire   +1 more source

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 ...
openaire   +1 more source

General Hypergeometric Functions of Matrices and their Connection to Representations of Linear Groups and Lie Algebras

Acta Applicandae Mathematicae, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Linear representations of the Lie algebra of the diffeomorphism group in $$\mathbb{R}^d$$

Theoretical and Mathematical Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

The Lie algebra of a linear algebraic group

2011
openaire   +1 more source

The Lie algebra of a linear algebraic group

1995
openaire   +1 more source

Ordinary, Partial, Linear, and non-Linear Differential Equations In the Wake of Symmetry Methods Initiated by Sophus Lie (Hydon) Followed By Lie Groups, Lie Algebras, and Their Applications (Gilmore)

2013
openaire   +1 more source