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...

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

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...

\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...

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

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

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

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

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

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

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

trivially holds at orders ℏ 0 , ℏ {\displaystyle \hbar ^{0},\hbar } ). Lie bialgebra Yangian Reidemeister move Quasitriangular Hopf algebra H.-D. Doebner,...

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...

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...

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

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

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...

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

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

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...

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

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...

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

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...