Equivariant homologies for operator algebras; a survey
محورهای موضوعی : Functional analysis
A. Shirinkalam
1
(Department of mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran)
کلید واژه: group action, Equivariant Hochschild cohomology, equivariant $L^2$-cohomology, graded $ L^2 $-Betti number, graded algebra,
چکیده مقاله :
‎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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