Chern特征标、Hopf代数和BRS上同调
Chern character, Hopf algebras, and BRS cohomology
摘要：
本文给出了一个循环上同调的陈特征标的构造，它涉及任意数目的反变或协变结合代数。这是一个推广的双变陈特征的代数在以前的文件中介绍，基于Quillen超连接和热核正则化。然后，我们适应的形式主义的Hopf代数的Connes-Moscovici意义下的循环上同调。这就产生了代数A上的“等变K-圈”的陈特征标，推广了Connes-Moscovici特征映射。在等变谱三元组验证一些额外的条件的情况下，我们还展示了第二特征类。后者与拓扑学无关，而是定义了A的高等代数K-理论的特征映射。在自旋流形的经典情形下，我们用量子场论中的BRS上同调来计算和解释这些次级类。
英文摘要：
We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological algebras introduced in a previous paper, based on Quillen superconnections and heat-kernel regularization. Then we adapt the formalism to the cyclic cohomology of Hopf algebras in the sense of Connes-Moscovici. This yields a Chern character for ``equivariant K-cycles'' over a bornological algebra A, generalizing the Connes-Moscovici characteristic maps. In the case of equivariant spectral triples verifying some additional conditions, we also exhibit secondary characteristic classes. The latter are not related to topology but rather define characteristic maps for the higher algebraic K-theory of A. In the classical case of spin manifolds, we compute and interpret these secondary classes in terms of BRS cohomology in Quantum Field Theory.
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