Weak Hopf Algebras and Some New Solutions of the Quantum Yang–Baxter Equation,

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 constructed from some weak Hopf algebras, in particular, when the weak Hopf algebra is a finite Clifford monoid algebra.