Let H be a Hopf algebra with invertible antipode. Two different actions of the braid group B n on H ⊗n are described. These are representations of the braid group associated to solutions of the Yang-Baxter equation. By passing to a submodule for one action and to a quotient module for the other, we
Classical Yang–Baxter Equation and the A∞-Constraint
✍ Scribed by A. Polishchuk
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 259 KB
- Volume
- 168
- Category
- Article
- ISSN
- 0001-8708
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✦ Synopsis
We show that elliptic solutions of classical Yang-Baxter equation (CYBE) can be obtained from triple Massey products on an 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.
📜 SIMILAR VOLUMES
In this paper, the concepts of a weak Hopf algebra and a quasi-braided almost bialgebra are introduced. It is shown that the quantum quasi-doubles of some weak Hopf algebras are quasi-braided almost bialgebras. This fact implies that some new solutions of the quantum Yang᎐Baxter equation can be cons
The authors showed previously on Frobenius algebras and quantum Yang-Baxter . equation, II, preprint, TRITA-MAT-1995, February 1995 that every Frobenius algebra over a commutative ring defines a solution of the quantum Yang-Baxter equation. Applying this result to Hopf algebras over commutative ring