Algebras and Representation Theory

, Volume 4, Issue 1, pp 55–76

Quantum Symmetric Algebras

  • Delia Flores de Chela
  • James A. Green

DOI: 10.1023/A:1009953611721

Cite this article as:
de Chela, D.F. & Green, J.A. Algebras and Representation Theory (2001) 4: 55. doi:10.1023/A:1009953611721


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.

quantum group Cartan datum twisted bi-algebra 

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Delia Flores de Chela
    • 1
  • James A. Green
    • 2
  1. 1.School of MathematicsUniversidad Central de VenezuelaCaracasVenezuela
  2. 2.OxfordEngland

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