Work

A C*-cover lattice dichotomy

Year: 2026

Type: preprint

Abstract: In this paper, we show that the lattice of C*-covers of a non-selfadjoint operator algebra is either one point or uncountable. We prove that there are non-selfadjoint operator algebras with a one-point lattice in two ways: as an explicit subalgebra of the C*-algebra of a universal contraction, and via a direct limit construction inspired by the work of Kirchberg and Wassermann for operator systems. We also establish that the C*-envelope need not have an immediate successor C*-cover in the lattice, and that a semi-Dirichlet non-selfadjoint operator algebra never has a one-point lattice.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2601.05088

Authors: Humeniuk, Adam, Ramsey, Christopher, Scherer, Marcel

Institution: Mount Royal University

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Natural Sciences and Engineering Research Council of Canada

Awards: G6420667649, Hilberträume mit reproduzierendem Kern und Dilatationstheorie

OpenAlex ID: W7120218358

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