Polynomial growth of discrete quantum groups, topological dimension of the dual and *-regularity of the Fourier algebra

Alessandro D'Andrea; Claudia Pinzari; Stefano Rossi

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arXiv · 1602.07496

Polynomial growth of discrete quantum groups, topological dimension of the dual and *-regularity of the Fourier algebra

Alessandro D'Andrea·Claudia Pinzari·Stefano Rossi

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Abstract

Banica and Vergnioux have shown that the dual discrete quantum group of a compact simply connected Lie group has polynomial growth of order the real manifold dimension. We extend this result to a general compact group and its topological dimension, by connecting it with the Gelfand-Kirillov dimension of an algebra. Furthermore, we show that polynomial growth for a compact quantum group G of Kac type implies *-regularity of the Fourier algebra A(G), that is every closed ideal of C(G) has a dense intersection with A(G). In particular, A(G) has a unique C*-norm.

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Alessandro D'Andrea, Claudia Pinzari, Stefano Rossi. 2016-02-24. Polynomial growth of discrete quantum groups, topological dimension of the dual and *-regularity of the Fourier algebra. https://arxiv.org/abs/1602.07496

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