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1. Representation theory of Hopf algebras: In 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 over a field K is a K-vector space V with an action H ... [100%] 2023-11-22 [Hopf algebras] [Representation theory]...

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1. Hopf algebra: bi-algebra, hyperalgebra A graded module $ A $ over an associative-commutative ring $ K $ with identity, equipped simultaneously with the structure of an associative graded algebra $ \mu : \ A \otimes A \rightarrow A $ with identity (unit element) $ \iota : \ K \rightarrow A $ and ... (Mathematics) [100%] 2023-10-17
2. Hopf algebra: In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism ... (Construction in algebra) [100%] 2023-11-09 [Hopf algebras] [Representation theory]...
3. Hopf algebra: In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism ... (Construction in algebra) [100%] 2023-12-23 [Hopf algebras] [Monoidal categories]...
4. Algebraic algebra: An algebra with associative powers (in particular, an associative algebra) over a field in which all elements are algebraic: an element $a$ of the algebra $A$ is called algebraic over the field $F$ if the subalgebra $F$ generated by $a ... (Mathematics) [86%] 2023-10-13
5. Group Hopf algebra: In mathematics, 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 in the theory of quantum groups. [81%] 2023-12-15 [Hopf algebras] [Quantum groups]...
6. Taft Hopf algebra: In algebra, a Taft Hopf algebra is a Hopf algebra introduced by Earl Taft (1971) that is neither commutative nor cocommutative and has an antipode of large even order. Suppose that k is a field with a primitive n'th ... [81%] 2024-01-03 [Hopf algebras]
7. Taft Hopf algebra: In algebra, a Taft Hopf algebra is a Hopf algebra introduced by Earl Taft (1971) that is neither commutative nor cocommutative and has an antipode of large even order. Suppose that k is a field with a primitive n'th ... [81%] 2022-12-03 [Hopf algebras]
8. Braided Hopf algebra: In mathematics, a braided Hopf algebra is a Hopf algebra in a braided monoidal category. The most common braided Hopf algebras are objects in a Yetter–Drinfeld category of a Hopf algebra H, particularly the Nichols algebra of a braided ... [81%] 2022-12-24 [Hopf algebras]
9. Leibniz-Hopf algebra: Let $\mathbf{Z}\langle Z \rangle$ be the free associative algebra on $Z = \{Z_1,Z_2,\ldots\}$ over the integers. Give $\mathbf{Z}\langle Z \rangle$ a Hopf algebra structure by means of the following co-multiplication, augmentation, and antipode: $$ \mu ... (Mathematics) [81%] 2023-05-16 [TeX done]
10. Ribbon Hopf algebra: A ribbon Hopf algebra ( A , ∇ , η , Δ , ε , S , R , ν ) {\displaystyle (A,\nabla ,\eta ,\Delta ,\varepsilon ,S,{\mathcal {R}},\nu )} is a quasitriangular Hopf algebra which possess an invertible central element ν {\displaystyle \nu } more commonly known as the ribbon element, such that the ... (Algebraic structure) [81%] 2024-11-13 [Hopf algebras]
11. Leibniz-Hopf algebra: Let $\mathbf{Z}\langle Z \rangle$ be the free associative algebra on $Z = \{Z_1,Z_2,\ldots\}$ over the integers. Give $\mathbf{Z}\langle Z \rangle$ a Hopf algebra structure by means of the following co-multiplication, augmentation, and antipode: $$ \mu ... [81%] 2026-04-09 [TeX done] [Mathematics]...
12. Pareigis Hopf algebra: In algebra, the Pareigis Hopf algebra is the Hopf algebra over a field k whose left comodules are essentially the same as complexes over k, in the sense that the corresponding monoidal categories are isomorphic. It was introduced by (Pareigis ... [81%] 2026-03-14 [Hopf algebras]
13. Ribbon Hopf algebra: A ribbon Hopf algebra (A,∇,η,Δ,ε,S,ℛ,ν) is a quasitriangular Hopf algebra which possess an invertible central element ν more commonly known as the ribbon element, such that the following conditions hold: where u=∇(S⊗id)(ℛ21). Note that the element u ... [81%] 2026-03-14 [Hopf algebras]
14. Weak Hopf algebra: In mathematics, weak bi-algebras are a generalization of bialgebras that are both algebras and coalgebras but for which the compatibility conditions between the two structures have been "weakened". In the same spirit, weak Hopf algebras are weak bialgebras together ... [81%] 2026-03-14 [Hopf algebras]
15. Hopf (Familienname): Hopf ist eine Variante des Familiennamens Höpfner. Ein Hopfner betrieb im Mittelalter den Beruf des Hopfenbauers, Hopfenhändlers oder hatte auf andere Weise etwas mit Hopfen zu tun. (Familienname) [76%] 2024-01-19
16. Quasi-triangular Hopf algebra: dual quasi-triangular Hopf algebra, co-quasi-triangular Hopf algebra, quantum group A quantum group in the strict sense, i.e. a Hopf algebra $H$ equipped with a further (co-) quasi-triangular structure $\mathcal{R}$ obeying certain axioms such that ... (Mathematics) [70%] 2021-12-23
17. Hopf algebra of permutations: In algebra, the Malvenuto–Poirier–Reutenauer Hopf algebra of permutations or MPR Hopf algebra is a Hopf algebra with a basis of all elements of all the finite symmetric groups Sn, and is a non-commutative analogue of the Hopf ... [70%] 2023-12-12 [Hopf algebras]
18. Lie algebra, algebraic: The Lie algebra of an algebraic subgroup (see Algebraic group) of the general linear group of all automorphisms of a finite-dimensional vector space $V$ over a field $k$. If $\mathfrak g$ is an arbitrary subalgebra of the Lie algebra ... (Mathematics) [70%] 2023-10-17
19. Algebra: Algebra is a branch of mathematics. The term is used in combinations such as homological algebra, commutative algebra, linear algebra, multilinear algebra, and topological algebra. (Mathematics) [65%] 2023-10-17 [Algebra]