𝐿²-homology over traced *-algebras

DOI10.1090/S0002-9947-97-01910-7zbMath0878.46053OpenAlexW1487058424MaRDI QIDQ4336563

William L. Paschke

Publication date: 13 May 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-01910-7

zbMATH Keywords

Euler characteristictensor productsvon Neumann dimensionexact sequenceBetti numbersKünneth formula*-representationhomology spaces\(A\)-invariant subspacesprojective \(A\)-modulestracial positive linear functionalunital complex *-algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Representations of topological algebras with involution (46K10) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25)

Related Items (1)

Tracial algebras and an embedding theorem

Cites Work

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• \(L_ 2\)-cohomology and group cohomology
• On the fundamental group of a compact Kähler manifold
• De Rham-Hodge theory for \(L^2\)-cohomology of infinite coverings
• An invariant for finitely presented \(\mathbb{C} G\)-modules
• Group cohomology, harmonic functions and the first \(L^ 2\)-Betti number
• Bounds on the von Neumann dimension of \(L^ 2\)-cohomoloy and the Gauss- Bonnet theorem for open manifolds
• Quantum Weyl algebras and deformations of \(U(G)\)
• VON NEUMANN DIMENSION AND THE HOMOLOGY OF COVERING SPACES
• A numerical invariant for finitely generated groups via actions on graphs.

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