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...

In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative)...

A quasi-triangular quasi-Hopf algebra is a specialized form of a quasi-Hopf algebra defined by the Ukrainian mathematician Vladimir Drinfeld in 1989....

the quasi-triangular quasi-Hopf algebra. Such a twist is known as an admissible (or Drinfeld) twist. Quasi-triangular quasi-Hopf algebra Ribbon Hopf algebra...

Hopf algebra ( A , ∇ , η , Δ , ε , S , R , ν ) {\displaystyle (A,\nabla ,\eta ,\Delta ,\varepsilon ,S,{\mathcal {R}},\nu )} is a quasitriangular Hopf...

solvability of statistical mechanical models. He also generalized Hopf algebras to quasi-Hopf algebras and introduced the study of Drinfeld twists, which can be...

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...

Heyting algebra Hopf algebra Non-associative algebra Outline of algebra Relational algebra Sigma-algebra Symmetric algebra T-algebra Tensor algebra When...

quasisymmetric functions. One example of this is the peak algebra. The Malvenuto–Reutenauer algebra is a Hopf algebra based on permutations that relates the rings...

product Hopf algebra Quasi-Frobenius Lie algebra Dagger compact category Haim, Mariana (2007). "Group-like algebras and Hadamard matrices". J. Algebra. 308...

noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix...

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...

comodules over a Hopf algebroid are the purely algebraic analogue of this construction, giving a purely algebraic description of quasi-coherent sheaves...

coefficients from integers to the rational numbers. To any group ring or Hopf algebra is associated its representation ring or "Green ring". The representation...

Quasi-Hopf algebra C. Kassel. "Quantum Groups". Graduate Texts in Mathematics Springer-Verlag. ISBN 0387943706 Vladimir Drinfeld, Quasi-Hopf algebras...

symmetric Lie algebra Poisson algebra Pre-Lie algebra Quantum groups Moyal algebra Quasi-Frobenius Lie algebra Quasi-Lie algebra Restricted Lie algebra Serre...

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties...

"Bialgebras and Hopf algebras. Motivation, definitions, and examples". Algebras, Rings and Modules Lie Algebras and Hopf Algebras. American Mathematical...

"On quasitriangular quasi-Hopf algebras and on a group that is closely connected with Gal(Q/Q)", Rossiĭskaya Akademiya Nauk. Algebra i Analiz (in Russian)...

Representation theory of Hopf algebras General Associative property, Associator Heap (mathematics) Magma (algebra) Loop (algebra), Quasigroup Nonassociative...

studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements...

the quasi-triangular Hopf algebras, and then performing what is called a quantum deformation to obtain the quantum universal enveloping algebra, or quantum...

In mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups R i...

Hopf algebras of functions. A finite commutative group scheme over a field corresponds to a finite dimensional commutative cocommutative Hopf algebra...

In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible...

In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with...

Conway polynomials. Although finite fields are not algebraically closed, they are quasi-algebraically closed, which means that every homogeneous polynomial...

extra condition that an algebraic space has to be quasi-separated, meaning that the diagonal map is quasi-compact. Algebraic spaces are similar to schemes...

In 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...

In abstract algebra, a semiring is an algebraic structure. It is a generalization of a ring, dropping the requirement that each element must have an additive...