Abstract
The ‘plus part’ U + of a quantum group U q (g) has been identified by M. Rosso with a subalgebra G sym of an algebra G which is a quantized version of R. Ree's shuffle algebra. Rosso has shown that G sym and G – and hence also Hopf algebras which are analogues of quantum groups – can be defined in a much wider context. In this paper we study one of Rosso's quantizations, which depends on a family of parameters t ij . G sym is determined by a family of matrices Ωα whose coefficients are polynomials in the t ij . The determinants of the Ωα factorize into a number of irreducible polynomials, and our main Theorem 5.2a gives strong information on these factors. This can be regarded as a first step towards the (still very distant!) goal, the classification of the symmetric algebras G sym which can be obtained by giving special values to the parameters t ij .
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de Chela, D.F., Green, J.A. Quantum Symmetric Algebras. Algebras and Representation Theory 4, 55–76 (2001). https://doi.org/10.1023/A:1009953611721
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DOI: https://doi.org/10.1023/A:1009953611721