Quasidiagonal solutions of the Yang-Baxter equation, quantum groups and quantum super groups (Q1273490)

The author investigates in great detail quantum and quantum super groups, especially quasidiagonal solutions of the Yang-Baxter equation. The corresponding bialgebras are standard deformations of \(\text{GL}(n)\) and \(\text{GL}(m|n)\). It is also shown how the existence of zero divisors in some of these algebras is related to the combinatorics of their related matrix, providing a necessary and sufficient condition for the bialgebras to be a domain. Poincaré series are considered and a Hopf algebra structure to quotients of theses bialgebras is provided in an explicit way. The lift of the Hopf algebra structure provides problems, working only by localization.