论文标题
C* - 代数的Gysin序列和SU（2） - 对称性
Gysin sequences and SU(2)-symmetries of C*-algebras
论文作者
论文摘要
通过研究C*-Algebras的对称性以及由多元操作员理论的对称性的动机，我们介绍了Hilbert Space的SU（2） - 等级次级产品的概念。我们通过Kasparov的双变量K理论分析了由此产生的Toeplitz和Cuntz-Pimsner代数，并提供有关其拓扑不变的结果。特别是，从SU（2）的不可约表示，我们表明相应的Toeplitz代数与复杂数字的代数等同于KK。通过这种方式，我们获得了六个项的精确序列的k组序列，该序列包含欧拉类的非共同类似物。
Motivated by the study of symmetries of C*-algebras, as well as by multivariate operator theory, we introduce the notion of an SU(2)-equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz-Pimsner algebras and provide results about their topological invariants through Kasparov's bivariant K-theory. In particular, starting from an irreducible representation of SU(2), we show that the corresponding Toeplitz algebra is equivariantly KK-equivalent to the algebra of complex numbers. In this way, we obtain a six term exact sequence of K-groups containing a noncommutative analogue of the Euler class.
