Associative Triples and Yang-baxter Equation
نویسنده
چکیده
We introduce triples of associative algebras as a tool for building solutions to the Yang-Baxter equation. It turns out that the class of R-matrices thus obtained is related to the Hecke condition whose generalization subject to an associative triple is proposed. R-matrices for a wide class of Belavin-Drinfel’d triples for the sln(C) Lie algebras are derived.
منابع مشابه
O-operators on Associative Algebras and Associative Yang-baxter Equations
We introduce the concept of an extended O-operator that generalizes the wellknown concept of a Rota-Baxter operator. We study the associative products coming from these operators and establish the relationship between extended O-operators and the associative Yang-Baxter equation, extended associative Yang-Baxter equation and generalized Yang-Baxter equation.
متن کاملClassical Yang-Baxter equation and the A∞-constraint
We show that elliptic solutions of classical Yang-Baxter equation (CYBE) can be obtained from triple Massey products on elliptic curve. We introduce the associative version of this equation which has two spectral parameters and construct its elliptic solutions. We also study some degenerations of these solutions.
متن کاملMassey Products on Cycles of Projective Lines and Trigonometric Solutions of the Yang-baxter Equations
We show that a nondegenerate unitary solution r(u, v) of the associative Yang-Baxter equation (AYBE) for Mat(N, C) (see [4]) with the Laurent series at u = 0 of the form r(u, v) = 1⊗1 u + r0(v) + . . . satisfies the quantum Yang-Baxter equation, provided the projection of r0(v) to slN ⊗ slN has a period. We classify all such solutions of the AYBE extending the work of Schedler [5]. We also char...
متن کاملHom-quantum Groups Ii: Cobraided Hom-bialgebras and Hom-quantum Geometry
A class of non-associative and non-coassociative generalizations of cobraided bialgebras, called cobraided Hom-bialgebras, is introduced. The non-(co)associativity in a cobraided Hom-bialgebra is controlled by a twisting map. Several methods for constructing cobraided Hombialgebras are given. In particular, Hom-type generalizations of FRT quantum groups, including quantum matrices and related q...
متن کاملDouble Constructions of Frobenius Algebras and Connes 2-cocycles and Their Duality
We construct an associative algebra with a decomposition into the direct sum of the underlying vector spaces of another associative algebra and its dual space such that both of them are subalgebras and the natural symmetric bilinear form is invariant or the natural antisymmetric bilinear form is a Connes 2-cocycle. The former is called a double construction of Frobenius algebra and the latter i...
متن کامل