Approximating the group algebra of the lamplighter by infinite matrix products

DOI10.1515/forum-2020-0141OpenAlexW3031998918MaRDI QIDQ2155610

Pere Ara, Joan Claramunt

Publication date: 15 July 2022

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.12374

zbMATH Keywords

rank functionlamplighterAtiyah conjecture\(\ell^2\)-Betti number*-regular closure

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Twisted and skew group rings, crossed products (16S35) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (1)

Malcolmson semigroups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Atiyah conjecture and Artinian rings.
• On Turing dynamical systems and the Atiyah problem
• \(L^2\)-Betti numbers arising from the lamplighter group
• The regular algebra of a quiver.
• The \(C^*\)-algebras associated with minimal homeomorphisms of the Cantor set
• Matrix rings over *-regular rings and pseudo-rank functions
• Determining homomorphisms to skew fields
• Integrality of \(L^2\)-Betti numbers
• The spectral measure of certain elements of the complex group ring of a wreath product
• Topics in orbit equivalence
• Sylvester rank functions for amenable normal extensions
• The strong Atiyah and Lück approximation conjectures for one-relator groups
• Irrational \(l^2\) invariants arising from the lamplighter group
• Algebraic entropy of amenable group actions
• On a question of Atiyah
• Lamplighter groups and von Neumann‘s continuous regular ring
• Rational group ring elements with kernels having irrational dimension
• A Course in Abstract Harmonic Analysis
• Closed manifolds with transcendentalL²-Betti numbers:
• On the topological stable rank of certain transformation group C*-algebras
• Uniqueness of the von Neumann Continuous Factor
• Partial Dynamical Systems, Fell Bundles and Applications
• ORDERED BRATTELI DIAGRAMS, DIMENSION GROUPS AND TOPOLOGICAL DYNAMICS
• Sylvester matrix rank functions on crossed products
• Bivariant and extended Sylvester rank functions
• The Realization Problem for some wild monoids and the Atiyah Problem
• Algèbres Commutatives Engendrées Par Leurs Éléments Idempotents
• \(C^*\)-algebras by example
• The lamplighter group as a group generated by a 2-state automaton, and its spectrum
• L2-Betti Numbers and their Analogues in Positive Characteristic

This page was built for publication: Approximating the group algebra of the lamplighter by infinite matrix products