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.
Quasidiagonal Solutions of the Quantum Yang-Baxter equation, Quantum Groups and Quantum Super Groups
CARNOVALE, GIOVANNA
1998
Abstract
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.Pubblicazioni consigliate
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