Quantum ax + b Group as Quantum Automorphism Group of k[x]

1998/07/31 by Shuzhou Wang
Mathematics · #math.OA #math.QA

paper · pdf

published as Communications in Algebra 30(4) (2002), 1807-1816 · AMSLATEX, 9 papges

arxiv created 2002/05/06 · arxiv updated 2009/11/30

Abstract

By introducing a result that guarantees a given bialgebra to be a Hopf algebra under a natural condition, we show that the quantum automorphism group of the algebra k[x] of polynomials over a field k (of any characteristic) is the universal quantum a x + b group, generalizing the fact that the automorphism group of k[x] is the a x + b group. The q-deformation of the a x + b group is then seen as one among a certain family \mathcal A_{q, n} of quantum subgroups of this universal quantum group.

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