In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative)...
35 KB (4,397 words) - 17:50, 19 August 2024
associative algebra, the coalgebra must be co-associative, and, if the algebra is unital, then the co-algebra must be co-unital as well. A Hopf algebra is a...
30 KB (4,256 words) - 10:18, 18 August 2024
Quantum group (redirect from Quantized universal enveloping algebra)
noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix...
30 KB (4,983 words) - 19:49, 25 July 2024
be extended by giving an antipode to create a Hopf algebra structure. Note: In this article, all algebras are assumed to be unital and associative. The...
23 KB (4,160 words) - 15:09, 12 January 2024
In mathematics, a Hopf algebra, H, is quasitriangular if there exists an invertible element, R, of H ⊗ H {\displaystyle H\otimes H} such that R Δ ( x...
4 KB (770 words) - 18:29, 19 September 2023
Group ring (section Hopf algebra)
as a group algebra, for it is indeed an algebra over the given ring. A group algebra over a field has a further structure of a Hopf algebra; in this case...
21 KB (3,985 words) - 12:37, 31 May 2024
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 (1,180 words) - 00:11, 11 November 2019
the group Hopf algebra of a given group is a certain construct related to the symmetries of group actions. Deformations of group Hopf algebras are foundational...
7 KB (1,201 words) - 06:43, 23 December 2023
both algebras and coalgebras but for which the compatibility conditions between the two structures have been "weakened". In the same spirit, weak Hopf algebras...
7 KB (1,312 words) - 00:33, 12 December 2022
algebra A p ∗ {\displaystyle {\mathcal {A}}_{p}^{*}} (also denoted A ∗ {\displaystyle {\mathcal {A}}^{*}} ) is a graded noncommutative Hopf algebra which...
5 KB (818 words) - 16:28, 22 May 2024