abstract algebra, a representation of a Hopf algebra is a representation of its underlying associative algebra. That is, a representation of a Hopf algebra H...
6 KB (1,181 words) - 18:43, 30 November 2024
satisfying a certain property. The representation theory of a Hopf algebra is particularly nice, since the existence of compatible comultiplication, counit...
35 KB (4,397 words) - 17:17, 1 February 2025
SU(2) Representation theory of the Lorentz group Representation theory of Hopf algebras Adjoint representation of a Lie group List of Lie group topics Symmetry...
34 KB (5,246 words) - 08:31, 14 January 2025
associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which elements of a group...
56 KB (7,269 words) - 14:03, 18 May 2025
polynomial of a matrix in one variable. Representation theory Intertwiner Representation theory of Hopf algebras Lie algebra representation Schur’s lemma...
7 KB (1,069 words) - 10:21, 30 June 2021
hence avoids the use of auxiliary Grassmann numbers. Graded vector space Lie algebra representation Representation theory of Hopf algebras v t e v t e...
3 KB (420 words) - 00:48, 29 March 2024
article associative algebras are assumed to have a multiplicative identity, denoted 1; they are sometimes called unital associative algebras for clarification...
31 KB (4,261 words) - 10:53, 26 May 2025
in algebra to examine the structure of groups. There are also applications in harmonic analysis and number theory. For example, representation theory is...
105 KB (21,294 words) - 10:21, 1 April 2025
enveloping algebras are used in the representation theory of Lie groups and Lie algebras. For example, Verma modules can be constructed as quotients of the universal...
51 KB (8,954 words) - 11:11, 9 February 2025
discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential...
195 KB (20,026 words) - 13:12, 7 May 2025
complex group ring C[G]. The importance of the group algebra is that it captures the unitary representation theory of G as shown in the following Theorem...
9 KB (1,339 words) - 18:05, 11 March 2025
in the representation theory of semisimple Lie algebras (or the closely related representation theory of compact Lie groups), the weights of the dual...
10 KB (1,699 words) - 19:20, 8 October 2024
to other categories in abstract algebra: associative algebras, rings, Lie algebras, Lie superalgebras, Hopf algebras to name some. Representations or...
22 KB (3,061 words) - 16:41, 24 April 2025
(mathematics) Representation theory of Hopf algebras General Associative property, Associator Heap (mathematics) Magma (algebra) Loop (algebra), Quasigroup...
12 KB (1,129 words) - 10:50, 10 October 2024
that every Lie algebra is contained in the Lie algebra associated to some associative algebra. The representation theory of Lie algebras plays an important...
61 KB (10,480 words) - 11:37, 29 May 2025
Discrete series representation Principal series representation Borel–Weil–Bott theorem Algebra representation Representation theory of Hopf algebras Quiver (mathematics)...
2 KB (195 words) - 18:57, 7 December 2024
results of Eberhard Hopf for Riemann surfaces of negative curvature. Markov chains form a common context for applications in probability theory. Ergodic...
26 KB (3,727 words) - 14:43, 28 April 2025
Ring (mathematics) (redirect from Ring (algebra))
Lie algebra. There exists some structure theory for such algebras that generalizes the analogous results for Lie algebras and associative algebras.[citation...
99 KB (13,738 words) - 11:06, 29 May 2025
Quantum group (redirect from Quantized universal enveloping algebra)
(which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum...
30 KB (4,983 words) - 17:53, 20 December 2024
associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which elements of a group...
24 KB (3,093 words) - 14:02, 18 May 2025
Field (mathematics) (redirect from Field theory (mathematics))
fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational...
87 KB (10,305 words) - 19:26, 28 May 2025
selfadjoint graded Hopf algebra that is both commutative and cocommutative. The study of symmetric functions is based on that of symmetric polynomials...
27 KB (3,850 words) - 18:08, 27 February 2024
Supergroup (physics) (redirect from Hopf superalgebra)
which plays a role similar to that of a Lie algebra for Lie groups in that they determine most of the representation theory and which is the starting point...
4 KB (615 words) - 10:31, 24 March 2025
p} , the Steenrod algebra A p {\displaystyle A_{p}} is the graded Hopf algebra over the field F p {\displaystyle \mathbb {F} _{p}} of order p {\displaystyle...
30 KB (5,577 words) - 03:49, 29 May 2025
→ A which may or may not be associative. Examples include Lie algebras, Jordan algebras, the octonions, and three-dimensional Euclidean space equipped...
25 KB (3,005 words) - 20:16, 18 February 2025
special kind of bilinear form which gives the algebras particularly nice duality theories. Frobenius algebras began to be studied in the 1930s by Richard...
22 KB (3,230 words) - 08:20, 9 April 2025
Hypercomplex number (redirect from Hypercomplex algebras)
Clifford algebra over the reals—i.e. coefficients of elements of the algebra are to be real numbers. These algebras, called geometric algebras, form a...
27 KB (3,215 words) - 12:59, 17 May 2025
Module (mathematics) (redirect from Module theory)
related to the representation theory of groups. They are also one of the central notions of commutative algebra and homological algebra, and are used widely...
22 KB (3,091 words) - 12:09, 26 March 2025
between affine group schemes over k and commutative Hopf algebras over k. For example, the Hopf algebra corresponding to the multiplicative group Gm = GL(1)...
41 KB (6,000 words) - 12:59, 4 October 2024
Dual representation Hermite reciprocity Clebsch–Gordan coefficients Lie group representation Lie algebra representation Kronecker product Hopf algebra Serre...
16 KB (2,941 words) - 05:49, 19 May 2025