Quasi-triangular structures on Hopf algebras with positive bases

Details Quasi-triangular structures on Hopf algebras with positive bases Quasi-triangular structures on Hopf algebras with positive bases

1999-11-13

arxiv.org/abs/math/9911092v1

Mathematics

Quantum Algebra

Scientific paper

A basis B of a finite dimensional Hopf algebra H is said to be positive if all the structure constants of H relative to B are non-negative. A quasi-triangular structure $R\in H\otimes H$ is said to be positive with respect to B if it has non-negative coefficients in the basis $B \otimes B$ of $H\otimes H$. In our earlier work, we have classified all finite dimensional Hopf algebras with positive bases. In this paper, we classify positive quasi-triangular structures on such Hopf algebras. A consequence of this classification is a new way of constructing set-theoretical solutions of the Yang-Baxter equation.

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