physics, a representation of a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the...

representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra...

field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices...

mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to...

Lie groups form a class of topological groups, and the compact Lie groups have a particularly well-developed theory. Basic examples of compact Lie groups...

the representation theory of the Poincaré group is an example of the representation theory of a Lie group that is neither a compact group nor a semisimple...

of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the...

The Lorentz group is a Lie group of symmetries of the spacetime of special relativity. This group can be realized as a collection of matrices, linear transformations...

In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple...

Index of a Lie algebra Leibniz algebra Lie algebra cohomology Lie algebra extension Lie algebra representation Lie bialgebra Lie coalgebra Lie n-algebra...

This is a list of Lie group topics, by Wikipedia page. See Table of Lie groups for a list General linear group, special linear group SL2(R) SL2(C) Unitary...

differential geometry, an antifundamental representation of a Lie group is the complex conjugate of the fundamental representation, although the distinction between...

representations of the nontrivial central extension of the universal covering group of the Galilean group by the one-dimensional Lie group R, cf. the article...

particles to the structure of Lie groups and Lie algebras. According to this connection, the different quantum states of an elementary particle give...

tools in the representation theory of Lie groups and Lie algebras; they can also be used to study the algebraic topology of such groups and associated...

mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for such a relationship...

a description include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory...

In mathematics, a Lie group (pronounced /liː/ LEE) is a group that is also a differentiable manifold, such that group multiplication and taking inverses...

representations of the Lie group SL(2, R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish-Chandra (1952). We choose a basis H, X, Y...

study of the representation theory of Lie groups, the study of representations of SU(2) is fundamental to the study of representations of semisimple Lie groups...

Lie algebra representation associated to the dual of a Lie group representation is computed by the above formula. But the definition of the dual of a...

universal complexification of a real Lie group is given by a continuous homomorphism of the group into a complex Lie group with the universal property...

mathematics, the coadjoint representation K {\displaystyle K} of a Lie group G {\displaystyle G} is the dual of the adjoint representation. If g {\displaystyle...

of linear transformations of vector spaces Representation of a Lie group, a linear action of a Lie group on a vector space Lie algebra representation...

article gives a table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension;...

character of the unitary representation of a Lie group G on the space L2(Γ\G) of square-integrable functions, where Γ is a cofinite discrete group. The character...

mathematics, the representation theory of semisimple Lie algebras is one of the crowning achievements of the theory of Lie groups and Lie algebras. The theory...

identity mapping of V. A trivial representation of an associative or Lie algebra is a (Lie) algebra representation for which all elements of the algebra act...

is a basic result in the representation theory of Lie groups, showing how a family of representations can be obtained from holomorphic sections of certain...

(or reductive) Lie group, can be done for all. Therefore, once the role of some low-dimensional Lie groups such as GL(2) in the theory of modular forms...