Hopf algebra

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• Hopf algebra — In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital associative) algebra, a coalgebra, and has an antiautomorphism, with these structures compatible.Hopf algebras occur naturally in algebraic… …   Wikipedia

• Hopf-Algebra — Hopfalgebra berührt die Spezialgebiete Mathematik Abstrakte Algebra Lineare Algebra Kommutative Algebra ist Spezialfall von Bialgebra Eine Hopf Algebra – benannt …   Deutsch Wikipedia

• 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 Drinfel d category of a Hopf algebra H . Definition Let H be a Hopf algebra over a field k , and …   Wikipedia

• 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. DefinitionLet G be an arbitrary group …   Wikipedia

• Quasi-triangular Quasi-Hopf algebra — A quasi triangular quasi Hopf algebra is a specialized form of a quasi Hopf algebra defined by the Ukrainian mathematician Vladimir Drinfeld in 1989. It is also a generalized form of a quasi triangular Hopf algebra.A quasi triangular quasi Hopf… …   Wikipedia

• Quasitriangular Hopf algebra — In mathematics, a Hopf algebra, H, is quasitriangular[1] if there exists an invertible element, R, of such that for all , where Δ is the coproduct on H, and the linear map is …   Wikipedia

• Quasi-Hopf algebra — A quasi Hopf algebra is a generalization of a Hopf algebra, which was defined by the Russian mathematician Vladimir Drinfeld in 1989.A quasi Hopf algebra is a quasi bialgebra mathcal{B A} = (mathcal{A}, Delta, varepsilon, Phi)for which there… …   Wikipedia

• Ribbon Hopf algebra — A Ribbon Hopf algebra (A,m,Delta,u,varepsilon,S,mathcal{R}, u) is a Quasitriangular Hopf algebrawhich possess an invertible central element u more commonly known as the ribbon element, such that the following conditions hold:: u^{2}=uS(u), ; S(… …   Wikipedia

• Algebra (Begriffsklärung) — Algebra bezeichnet in der Mathematik: Algebra, ein Teilgebiet der Mathematik mit den weiteren Teilgebieten Elementare Algebra Abstrakte Algebra Lineare Algebra Kommutative Algebra Universelle Algebra Computeralgebra Außerdem bezeichnet man mit… …   Deutsch Wikipedia

• *-algebra — * ring= In mathematics, a * ring is an associative ring with a map * : A rarr; A which is an antiautomorphism, and an involution.More precisely, * is required to satisfy the following properties: * (x + y)^* = x^* + y^* * (x y)^* = y^* x^* * 1^* …   Wikipedia

• Algebra — Aryabhata I …   Deutsch Wikipedia