Torsion-freeness for fusion rings and tensor C*-categories
Torsion-freeness for fusion rings and tensor C*-categories
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DOI：
10.4171/jncg/322
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发表时间：
2015-11
影响因子：
0.9
通讯作者：
Yuki Arano;K. Commer
中科院分区：
文献类型：
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作者：
Yuki Arano;K. Commer
离散量子群的无挠性是由R. Meyer，以便为离散量子群制定一个版本的Baum-Connes猜想。本文引入抽象融合环的无挠性。我们证明了一个离散量子群是无挠的，如果它的相应的融合环是无挠的。在后一种情况下，我们说离散量子群是强无挠的。作为应用，我们证明了自由么正量子群的离散量子群是强无挠的，并且在笛卡尔积和自由积下离散量子群的无挠性是保持的.我们还讨论了抽象刚性张量C ~*-范畴的更一般情形下的挠自由性
Torsion-freeness for discrete quantum groups was introduced by R. Meyer in order to formulate a version of the Baum-Connes conjecture for discrete quantum groups. In this note, we introduce torsion-freeness for abstract fusion rings. We show that a discrete quantum group is torsion-free if its associated fusion ring is torsion-free. In the latter case, we say that the discrete quantum group is strongly torsion-free. As applications, we show that the discrete quantum group duals of the free unitary quantum groups are strongly torsion-free, and that torsion-freeness of discrete quantum groups is preserved under Cartesian and free products. We also discuss torsion-freeness in the more general setting of abstract rigid tensor C*-categories