Equivariant homologies for operator algebras; a survey
الموضوعات :
1 - Department of mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
الکلمات المفتاحية: group action, Equivariant Hochschild cohomology, equivariant $L^2$-cohomology, graded $ L^2 $-Betti number, graded algebra,
ملخص المقالة :
This is a survey of a variety of equivariant (co)homology theories for operator algebras. We briefly discuss a background on equivariant Hochschild cohomology. 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.
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