Polynomial growth of discrete quantum groups, topological dimension of the dual and *-regularity of the Fourier algebra
Polynomial growth of discrete quantum groups, topological dimension of the dual and *-regularity of the Fourier algebra
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离散量子群的多项式增长、傅里叶代数的对偶和*正则的拓扑维数
DOI：
10.5802/aif.3127
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
S. Rossi
中科院分区：
文献类型：
--
作者：
Alessandro D'Andrea;C. Pinzari;S. Rossi
Banica 和 Vergnioux 证明了紧单连通李群的对偶离散量子群具有实流形维数阶的多项式增长。我们通过将其与代数的 Gelfand-Kirillov 维数联系起来，将这个结果扩展到一般紧群及其拓扑维数。此外，我们证明 Kac 型紧量子群 G 的多项式增长意味着傅里叶代数 A(G) 的*-正则性，即 C(G) 的每个闭合理想都与 A(G) 存在稠密交集。特别是，A(G) 具有独特的 C* 范数。
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.