New solutions of the Yang - Baxter equation based on root of 1 representations of the para-Bose superalgebra

Abstract

Abstract. New solutions of the quantum Yang-Baxter equation, depending in general on three arbitrary parameters, are written down. They are based on the root of unity representations of the quantum orthosymplectic superalgebra U q [osp(1/2)] , which were found recently. Representations of the braid group B N are defined within any N th tensorial power of root of 1 U q [osp(1/2)] modules.