Equivariant homologies for operator algebras; a survey

Journal of Linear and Topological Algebra

دوره 11، شماره 02، شهریور 2022، صفحه 129-142   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2022.1957929.1493

نویسنده

A. Shirinkalam^*

Department of mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

چکیده

‎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.

کلیدواژه‌ها

Equivariant Hochschild cohomology؛ equivariant $L^2$-cohomology؛ group action؛ graded $ L^2 $-Betti number؛ graded algebra

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