算子代数的等变同调
Equivariant homologies for operator algebras
摘要：
本文综述了算子代数的各种等变（上）同调论。我们简要地讨论了等变理论的背景，如等变$K$ -理论和等变循环同调。主要讨论了von Neumann代数的子代数的等变$ L^2 $ -上同调和等变$ L^2 $ -贝蒂数的概念.对于分次$C^*$ -代数（群上的分次），我们给出了分次$ L^2 $ -上同调的概念及其与等变$L^2$ -上同调的关系.
英文摘要：
This is a survey of a variety of equivariant (co)homology theories for operator algebras. We briefly discuss a background on equivariant theories, such as equivariant $K$-theory and equivariant cyclic homology. As the main focus, we discuss a notion of equivariant $ L^2 $-cohomology and equivariant $ L^2 $-Betti numbers for subalgebras of a von Neumann algebra. For graded $C^*$-algebras (with grading over a group) we elaborate on a notion of graded $ L^2 $-cohomology and its relation to equivariant $L^2$-cohomology.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
