Quasidiagonal Solutions of the Quantum Yang-Baxter equation, Quantum Groups and Quantum Super Groups

This paper answers a few questions about algebraic aspects of bialgebras, associated with the family of solutions of the quantum Yang-Baxter equation in Acta Appl. Math. 41 (1995), pp. 57-98. We describe the relations of the bialgebras associated with these solutions and the standard deformations of GL,, and of the supergroup GL(m / n). We also show how the existence of zero divisors in some of these algebras are related to the combinatorics of their related matrix, providing a necessary and sufficient condition for the bialgebras to be a domain. We consider their Poincare series, and we provide a Hopf algebra structure to quotients of these bialgebras in an explicit way. We discuss the problems involved with the lift of the Hopf algebra structure, working only by localization