论文标题
荣誉论文：分级$ kk $的精确序列 - cuntz-pimsner代数的理论
Honours thesis: Exact sequences in graded $KK$-theory for Cuntz-Pimsner algebras
论文作者
论文摘要
在这篇论文中，我们概括了在Kumjian，Pask和Sims（2017）论文中获得的分级$ kk $理论中的六项精确序列，以允许使用非紧凑型左动作的对应关系。特别是，这使我们能够计算排列的$ kk $ - 行无限图的理论。我们开发了遵循Kumjian，Pask和Sims以及Pimsner（1997）的论点所必需的理论，并提供了有关希尔伯特模块的详细部分，$ C^*$ - 通讯，交叉产品，Toeplitz代数，Cuntz-Pimsner代数和$ KK $ - theore。
In this thesis we generalise the six-term exact sequence in graded $KK$-theory obtained in a paper of Kumjian, Pask and Sims (2017) to allow correspondences with non-compact left action. In particular, this allows us to compute the graded $KK$-theory of row-infinite graphs. We develop the theory necessary for following the arguments of Kumjian, Pask and Sims and of Pimsner (1997), with detailed sections on Hilbert modules, $C^*$-correspondences, Crossed products, Toeplitz algebras, Cuntz-Pimsner algebras and $KK$-theory.
