Quasi-triangular structures on Hopf algebras with positive bases
Abstract
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∈H⊗H
is said to be positive with respect to B if it has non-negative coefficients in the basis
B⊗B
of
H⊗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.