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Suppose that M is a finite-dimensional vector space over a field k and that R : M ⊗M −→M ⊗M is solution to the quantum Yang–Baxter equation(QYBE). The FRT construction [3] 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 Ã(R), which seems rather useful in computation [11]. The bialgebra A(R) is Hopf algebra only when M = (0), whereas the bialgebra Ã(R) may very well be a Hopf algebra. ∗Research supported in part by EPSRC †Research supported in part by NSF Grant no. DMS 870-1085

Solutions to the quantum Yang-Baxter equation having certain bialgebras as their reduced FRT construction