紧量子群上Dirac算子的K-同调类
K-homology class of the Dirac operator on a compact quantum group
AI总结：
本研究基于Nagy的KK等价结论，证明紧李群q形变G_q上Dirac算子的K-同调类对应经典情形，并得到Drinfeld扭关于q连续的相关结果。
摘要：
根据Nagy的研究结果，单连通半单紧李群G的q形变G_q上的连续函数构成的C*-代数与C(G)是KK等价的。我们证明，在该等价关系下，我们在先前论文中构造的G_q上Dirac算子的K-同调类，对应于经典Dirac算子的K-同调类。研究过程中我们还证明，通过适当选取U_q(g)与U(g)的完备化之间的同构，可以选取一族联系形变与经典余乘的Drinfeld扭，使得其关于q是连续的。
英文摘要：
By a result of Nagy, the C*-algebra of continuous functions on the q-deformation G_q of a simply connected semisimple compact Lie group G is KK-equivalent to C(G). We show that under this equivalence the K-homology class of the Dirac operator on G_q, which we constructed in an earlier paper, corresponds to that of the classical Dirac operator. Along the way we prove that for an appropriate choice of isomorphisms between completions of U_q(g) and U(g) a family of Drinfeld twists relating the deformed and classical coproducts can be chosen to be continuous in q.
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