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.
D'Andrea A., Pinzari C., Rossi S. (2017). Polynomial growth of discrete quantum groups, topological dimension of the dual and ∗-regularity of the Fourier algebra. ANNALES DE L'INSTITUT FOURIER, 67(5), 2003-2027 [10.5802/aif.3127].
Polynomial growth of discrete quantum groups, topological dimension of the dual and ∗-regularity of the Fourier algebra
D'Andrea A.;
2017
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.