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arXiv · 1902.03593

Equivariant homologies for operator algebras

Massoud Amini·Ahmad Shirinkalam
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Abstract

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.

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BibTeXRIS

Massoud Amini, Ahmad Shirinkalam. 2019-02-10. Equivariant homologies for operator algebras. https://arxiv.org/abs/1902.03593

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