The base change in the Atiyah and the Lück approximation conjectures

DOI10.1007/s00039-019-00487-3zbMath1453.20007OpenAlexW2922526935WikidataQ122978924 ScholiaQ122978924MaRDI QIDQ2416542

Andrei Jaikin-Zapirain

Publication date: 23 May 2019

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00039-019-00487-3

zbMATH Keywords

sofic groupsAtiyah conjectureLück approximation*-regular rings

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) General theory of von Neumann algebras (46L10) Linear operator approximation theory (47A58) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Cites Work

• On the exactness of products in the localization of (Ab.\(4^{\ast}\)) Grothendieck categories
• The Atiyah conjecture and Artinian rings.
• On Turing dynamical systems and the Atiyah problem
• Brauer induction for \(G_ 0\) of certain infinite groups
• The strong approximation conjecture holds for amenable groups
• A short proof of the approximation conjecture for amenable groups
• Determining homomorphisms to skew fields
• The maximal ring of quotients of a finite von Neumann algebra
• De Rham-Hodge theory for \(L^2\)-cohomology of infinite coverings
• Modules over crossed products
• Approximating \(L^ 2\)-invariants by their finite-dimensional analogues
• Integrality of \(L^2\)-Betti numbers
• Hyperlinearity, essentially free actions and \(L^2\)-invariants. The sofic property
• Tensor products of division algebras and fields.
• Approximation by subgroups of finite index and the Hanna Neumann conjecture
• Infinite dimensional representations of finite dimensional algebras and amenability
• The strong Atiyah conjecture for virtually cocompact special groups
• Irrational \(l^2\) invariants arising from the lamplighter group
• Connes embeddings and von Neumann regular closures of amenable group algebras
• Free lamplighter groups and a question of Atiyah
• Rational group ring elements with kernels having irrational dimension
• Closed manifolds with transcendentalL²-Betti numbers:
• Sofic groups and diophantine approximation
• Finite group extensions and the Atiyah conjecture
• Division Rings and Group von Neumann Algebras
• Approximating L²‐invariants and the Atiyah conjecture
• Metric Approximations of Wreath Products
• The Realization Problem for some wild monoids and the Atiyah Problem
• L2-Betti Numbers and their Analogues in Positive Characteristic
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The base change in the Atiyah and the Lück approximation conjectures