SOLUTIONS TO THE QUANTUM YANG-BAXTER EQUATION HAVING CERTAIN BIALGEBRAS AS THEIR REDUCED FRT CONSTRUCTION

摘要

Suppose that M is a finite-dimensional vector space over a field k and that R: M directX M → M directX M is solution to the quantum Yang-Baxter equation(QYBE). The FRT construction is a bialgebra A(R) associated with R in a natural way. There is a quotient of the FRT construction, referred to as the reduced FRT construction and denoted by A(R), which seems rather useful in computation. The bialgebra A(R) is Hopf algebra only when M = (0), whereas the bialgebra A(R) may very well be a Hopf algebra.