Quantum Symmetric Algebras
- Cite this article as:
- de Chela, D.F. & Green, J.A. Algebras and Representation Theory (2001) 4: 55. doi:10.1023/A:1009953611721
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The ‘plus part’ U+ of a quantum group Uq(g) has been identified by M. Rosso with a subalgebra Gsym of an algebra G which is a quantized version of R. Ree's shuffle algebra. Rosso has shown that Gsym 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 tij. Gsym is determined by a family of matrices Ωα whose coefficients are polynomials in the tij. 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 Gsym which can be obtained by giving special values to the parameters tij.