This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)
This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations.(December 2020) (Learn how and when to remove this message)
This article needs editing to comply with Wikipedia's Manual of Style. In particular, it has problems with Needs a rewrite for inappropriate first-person per MOS:PERSON and less self-referential textbook-style writing per MOS:NOTE. Please help improve the content.(December 2020) (Learn how and when to remove this message)
(Learn how and when to remove this message)
Lie groups and Lie algebras
Classical groups
General linear GL(n)
Special linear SL(n)
Orthogonal O(n)
Special orthogonal SO(n)
Unitary U(n)
Special unitary SU(n)
Symplectic Sp(n)
Simple Lie groups
Classical
An
Bn
Cn
Dn
Exceptional
G2
F4
E6
E7
E8
Other Lie groups
Circle
Lorentz
Poincaré
Conformal group
Diffeomorphism
Loop
Euclidean
Lie algebras
Lie group–Lie algebra correspondence
Exponential map
Adjoint representation
Killing form
Index
Simple Lie algebra
Loop algebra
Affine Lie algebra
Semisimple Lie algebra
Dynkin diagrams
Cartan subalgebra
Root system
Weyl group
Real form
Complexification
Split Lie algebra
Compact Lie algebra
Representation theory
Lie group representation
Lie algebra representation
Representation theory of semisimple Lie algebras
Representations of classical Lie groups
Theorem of the highest weight
Borel–Weil–Bott theorem
Lie groups in physics
Particle physics and representation theory
Lorentz group representations
Poincaré group representations
Galilean group representations
Scientists
Sophus Lie
Henri Poincaré
Wilhelm Killing
Élie Cartan
Hermann Weyl
Claude Chevalley
Harish-Chandra
Armand Borel
Glossary
Table of Lie groups
v
t
e
In mathematics and theoretical 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 group into the group of invertible operators on the vector space. Representations play an important role in the study of continuous symmetry. A great deal is known about such representations, a basic tool in their study being the use of the corresponding 'infinitesimal' representations of Lie algebras.
and 25 Related for: Representation of a Lie group information
representation (or adjoint action) ofaLiegroup G is a way of representing the elements of the group as linear transformations of the group'sLie algebra...
Liegroups form a class of topological groups, and the compact Liegroups have a particularly well-developed theory. Basic examples of compact Lie groups...
mathematical field ofrepresentation theory, group representations describe abstract groups in terms of bijective linear transformations ofa vector space to...
The Lorentz group is aLiegroupof symmetries of the spacetime of special relativity. This group can be realized as a collection of matrices, linear transformations...
a description include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory...
between Lie algebras and Liegroups is used in several ways, including in the classification ofLiegroups and the representation theory ofLiegroups. For...
differential geometry, an antifundamental representationofaLiegroup is the complex conjugate of the fundamental representation, although the distinction between...
In mathematics, aLiegroup (pronounced /liː/ LEE) is agroup that is also a differentiable manifold, such that group multiplication and taking inverses...
In representation theory ofLiegroups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representationofa semisimple...
This is a list ofLiegroup topics, by Wikipedia page. See Table ofLiegroups for a list General linear group, special linear group SL2(R) SL2(C) Unitary...
representations of the nontrivial central extension of the universal covering groupof the Galilean group by the one-dimensional Liegroup R, cf. the article...
mathematics, the representation theory of semisimple Lie algebras is one of the crowning achievements of the theory ofLiegroups and Lie algebras. The theory...
article gives a table of some common Liegroups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension;...
tools in the representation theory ofLiegroups and Lie algebras; they can also be used to study the algebraic topology of such groups and associated...
identity mapping of V. A trivial representationof an associative or Lie algebra is a (Lie) algebra representation for which all elements of the algebra act...
character of the unitary representationofaLiegroup G on the space L2(Γ\G) of square-integrable functions, where Γ is a cofinite discrete group. The character...
In mathematics, aLie algebra is semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any...
linear group GL(S) such that the element −1 is not in the kernel of ρ. If S is such arepresentation, then according to the relation between Liegroups and...
affine representationofa topological Liegroup G on an affine space A is a continuous (smooth) group homomorphism from G to the automorphism groupofA, the...