R-matrices and the Yang-Baxter equation on GNS representations of C-bialgebras

Let A be a C∗-algebra with a comultiplication ∆. For two states ω and ψ of A which satisfy certain conditions, we construct a unitary R-matrix R(ω, ψ) of the C∗-bialgebra (A,∆) on the tensor product of GNS representations associated with ω and ψ such that the set {R(ω, ψ) : ω, ψ} satisfies the Yang-Baxter equation. Mathematics Subject Classifications (2000). 16W35, 81R50, 46K10.