quasi-Hopf algebra

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• 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

• 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

• 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

• 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

• 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

• Quasi-bialgebra — In mathematics, quasi bialgebras are a generalization of bialgebras, which were defined by the Ukrainian mathematician Vladimir Drinfeld in 1990.A quasi bialgebra mathcal{B A} = (mathcal{A}, Delta, varepsilon, Phi) is an algebra mathcal{A} over a …   Wikipedia

• Nichols algebra — The Nichols algebra of a braided vector space (with the braiding often induced by a finite group) is a braided Hopf algebra which is denoted by and named after the mathematician Warren Nichols. It takes the role of quantum Borel part of a pointed …   Wikipedia

• Frobenius algebra — In mathematics, especially in the fields of representation theory and module theory, a Frobenius algebra is a finite dimensional unital associative algebra with a special kind of bilinear form which gives the algebras particularly nice duality… …   Wikipedia

• List of mathematics articles (Q) — NOTOC Q Q analog Q analysis Q derivative Q difference polynomial Q exponential Q factor Q Pochhammer symbol Q Q plot Q statistic Q systems Q test Q theta function Q Vandermonde identity Q.E.D. QED project QR algorithm QR decomposition Quadratic… …   Wikipedia

• Quantum group — In mathematics and theoretical physics, quantum groups are certain noncommutative algebras that first appeared in the theory of quantum integrable systems, and which were then formalized by Vladimir Drinfel d and Michio Jimbo. There is no single …   Wikipedia

• Bialgebra — In mathematics, a bialgebra over a field K is a structure which is both a unital associative algebra and a coalgebra over K , such that these structures are compatible.Compatibility means that the comultiplication and the counit are both unital… …   Wikipedia