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...
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In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative)...
35 KB (4,397 words) - 17:50, 19 August 2024
A quasi-triangular quasi-Hopf algebra is a specialized form of a quasi-Hopf algebra defined by the Ukrainian mathematician Vladimir Drinfeld in 1989....
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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...
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Hopf algebra ( A , ∇ , η , Δ , ε , S , R , ν ) {\displaystyle (A,\nabla ,\eta ,\Delta ,\varepsilon ,S,{\mathcal {R}},\nu )} is a quasitriangular Hopf...
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Vladimir Drinfeld (category Algebraic geometers)
solvability of statistical mechanical models. He also generalized Hopf algebras to quasi-Hopf algebras and introduced the study of Drinfeld twists, which can be...
9 KB (834 words) - 16:51, 29 June 2024
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...
30 KB (4,256 words) - 10:18, 18 August 2024
Heyting algebra Hopf algebra Non-associative algebra Outline of algebra Relational algebra Sigma-algebra Symmetric algebra T-algebra Tensor algebra When...
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Quasisymmetric function (redirect from Quasi-symmetric function)
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...
16 KB (2,178 words) - 18:35, 3 March 2024
product Hopf algebra Quasi-Frobenius Lie algebra Dagger compact category Haim, Mariana (2007). "Group-like algebras and Hadamard matrices". J. Algebra. 308...
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Quantum group (redirect from Quantized universal enveloping algebra)
noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix...
30 KB (4,983 words) - 19:49, 25 July 2024
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...
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comodules over a Hopf algebroid are the purely algebraic analogue of this construction, giving a purely algebraic description of quasi-coherent sheaves...
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Ring (mathematics) (redirect from Ring (algebra))
coefficients from integers to the rational numbers. To any group ring or Hopf algebra is associated its representation ring or "Green ring". The representation...
99 KB (13,632 words) - 08:46, 14 August 2024
Quasi-Hopf algebra C. Kassel. "Quantum Groups". Graduate Texts in Mathematics Springer-Verlag. ISBN 0387943706 Vladimir Drinfeld, Quasi-Hopf algebras...
8 KB (1,449 words) - 01:54, 25 April 2024
symmetric Lie algebra Poisson algebra Pre-Lie algebra Quantum groups Moyal algebra Quasi-Frobenius Lie algebra Quasi-Lie algebra Restricted Lie algebra Serre...
61 KB (10,457 words) - 02:56, 14 July 2024
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties...
49 KB (3,356 words) - 14:42, 23 February 2024
Bialgebra (redirect from Bi-algebra)
"Bialgebras and Hopf algebras. Motivation, definitions, and examples". Algebras, Rings and Modules Lie Algebras and Hopf Algebras. American Mathematical...
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Grothendieck–Teichmüller group (section Relation to algebraic topology via the little disks operads)
"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)...
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Representation theory of Hopf algebras General Associative property, Associator Heap (mathematics) Magma (algebra) Loop (algebra), Quasigroup Nonassociative...
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Lattice (order) (redirect from Lattice (algebra))
studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements...
40 KB (5,663 words) - 17:53, 6 June 2024
the quasi-triangular Hopf algebras, and then performing what is called a quantum deformation to obtain the quantum universal enveloping algebra, or quantum...
52 KB (9,256 words) - 21:27, 19 August 2024
Graded ring (redirect from Graded algebra)
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...
16 KB (2,821 words) - 20:02, 17 August 2024
Cartier duality (category Algebraic groups)
Hopf algebras of functions. A finite commutative group scheme over a field corresponds to a finite dimensional commutative cocommutative Hopf algebra...
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Quasigroup (redirect from Quasi-group)
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible...
31 KB (3,858 words) - 15:47, 16 July 2024
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...
18 KB (1,840 words) - 22:25, 14 August 2024
Finite field (section Quasi-algebraic closure)
Conway polynomials. Although finite fields are not algebraically closed, they are quasi-algebraically closed, which means that every homogeneous polynomial...
45 KB (6,162 words) - 13:35, 7 August 2024
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...
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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...
29 KB (5,008 words) - 02:32, 15 April 2024
Semiring (redirect from Rig (algebra))
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...
52 KB (8,051 words) - 01:50, 26 June 2024