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

Shuzhou Wang

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

Shuzhou Wang

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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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Shuzhou Wang. 2002-05-06. Quantum ax + b Group as Quantum Automorphism Group of k[x]. https://arxiv.org/abs/math/9807094

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