mathematics, quasi-bialgebras are a generalization of bialgebras: they were first defined by the Ukrainian mathematician Vladimir Drinfeld in 1990. A quasi-bialgebra...

In mathematics, a bialgebra over a field K is a vector space over K which is both a unital associative algebra and a counital coassociative coalgebra...

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

functor in monoidal categories. Commutator Non-associative algebra Quasi-bialgebra – discusses the Drinfeld associator Bremner, M.; Hentzel, I. (March...

mathematician Vladimir Drinfeld in 1989. A quasi-Hopf algebra is a quasi-bialgebra B A = ( A , Δ , ε , Φ ) {\displaystyle {\mathcal {B_{A}}}=({\mathcal...

\triangleleft )} is a pre-Lie algebra. Lie coalgebra Lie bialgebra Lie algebra cohomology Frobenius algebra Quasi-Frobenius ring Jacobson, Nathan, Lie algebras,...

coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antihomomorphism satisfying a certain...

bundle Lie algebra cohomology Lie algebra representation Lie algebroid Lie bialgebra Lie coalgebra Lie conformal algebra Lie superalgebra Abelian Lie algebra...

Quasigroups and their Representations. CRC Press. ISBN 978-1-58488-537-5. quasigroups "Quasi-group", Encyclopedia of Mathematics, EMS Press, 2001 [1994]...

(mathematics) Category theory Monoidal category Groupoid Group object Coalgebra Bialgebra Hopf algebra Magma object Torsion (algebra) Symbolic mathematics Finite...

comultiplication if it satisfies certain axioms. The resulting structure is called a bialgebra. To be consistent with the definitions of the associative algebra, the...

ISBN 978-3-540-64243-5. Steenbrink, J. (1977). "Intersection form for quasi-homogeneous singularities" (PDF). Compositio Mathematica. 34 (2): 211–223...

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

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Lambe, Larry A.; Radford, David E. (eds.), "Quasitriangular Algebras, Bialgebras, Hopf Algebras and The Quantum Double", Introduction to the Quantum Yang-Baxter...

isomorphic left and right adjoints. Bialgebra Frobenius category Frobenius norm Frobenius inner product Hopf algebra Quasi-Frobenius Lie algebra Dagger compact...

trivially holds at orders ℏ 0 , ℏ {\displaystyle \hbar ^{0},\hbar } ). Lie bialgebra Yangian Reidemeister move Quasitriangular Hopf algebra Yang–Baxter operator...

continuity, the comultiplication on C is coassociative. In general, C is not a bialgebra, and C0 is a Hopf *-algebra. Informally, C can be regarded as the *-algebra...

algebra cohomology Lie algebra extension Lie algebra representation Lie bialgebra Lie coalgebra Lie operad Particle physics and representation theory Orthogonal...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

ISBN 978-1-4398-5130-2 Hausmann, B. A.; Ore, Øystein (October 1937), "Theory of quasi-groups", American Journal of Mathematics, 59 (4): 983–1004, doi:10.2307/2371362...

if k is a finite field or an algebraically closed field (more generally quasi-algebraically closed field; cf. Tsen's theorem). Br ⁡ ( R ) {\displaystyle...

application to the quantum Yang–Baxter equation, the quantisation of Lie bialgebras and quantum Lévy area. Hudson, R. L.; Ion, P. D. F.; K. R. Parthasarathy...

algebra structure, making g {\displaystyle {\mathfrak {g}}} into a Lie bialgebra. Moreover, Drinfeld proved that there is an equivalence of categories...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

lifts, given the prescription above. See, however, the discussion of the bialgebra structure in the article on tensor algebras for a review of some of the...

a connection to the thermo field dynamics of Hiroomi Umezawa, using a bialgebra constructed from a two-time quantum theory. Hiley has stated that his...

transitive, and those two properties found together are sometimes called strict quasi-order. Classically this defines a strict total order – indeed strict total...