紧量子群上的Dirac算子
The Dirac operator on compact quantum groups
AI总结：
针对单连通单紧李群的q形变，构造了经典Dirac算子谱三元组的等谱等变量子版本，证明其与正则函数的对易子有界。
摘要：
针对任意单连通单紧李群G的q形变G_q（0<q<1），我们构造了一个等变谱三元组，它是G上由Dirac算子D定义的谱三元组的等谱形变。我们的量子Dirac算子D_q是被视为U(g)⊗Cl(g)中元素的D的酉扭。D_q与G_q上正则函数的对易子由两部分组成：一部分是经典对易子的扭，因此自动有界；第二部分由结合子与D的一个扩张的对易子表示。我们证明，在Drinfeld结合子的情形下，后一结合子也是有界的。
英文摘要：
For the q-deformation G_q, 0<q<1, of any simply connected simple compact Lie group G we construct an equivariant spectral triple which is an isospectral deformation of that defined by the Dirac operator D on G. Our quantum Dirac operator D_q is a unitary twist of D considered as an element of U(g)\otimes Cl(g). The commutator of D_q with a regular function on G_q consists of two parts. One is a twist of a classical commutator and so is automatically bounded. The second is expressed in terms of the commutator of the associator with an extension of D. We show that in the case of the Drinfeld associator the latter commutator is also bounded.
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