Work

Asymmetry of ℓ2‐cohomology via skewed Følner geometry

Year: 2026

Type: article

Abstract: We study the two ‐Dirichlet structures on a countable group arising from the left and right regular actions on . Although the left and right regular representations on are unitarily equivalent, the ‐Dirichlet subspaces of need not coincide. Our main result gives a complete classification of this asymmetry for countable amenable groups: The proof is based on a skewed Følner‐geometric mechanism, called a left scheme , combining summability of left boundaries with displacement under a right translation. We develop this mechanism generally and demonstrate it concretely in the Heisenberg group and amenable wreath products over . We also show that this mechanism has a dynamical counterpart in the theory of nonsingular Bernoulli shifts: every countable amenable group that is not an FC‐group admits Bernoulli schemes whose left shift is nonsingular, conservative and weakly mixing, whereas the right shift by some element is singular.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70523

Authors: Nachi Avraham‐Re'em, Zemer Kosloff

Institutions: Technion – Israel Institute of Technology, Hebrew University of Jerusalem, University of Bristol

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Israel Science Foundation

Awards: G1336153396, G9001169858