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arxiv: 2602.10616 · v3 · pith:ER2354HDnew · submitted 2026-02-11 · 🧮 math.OA · math.DS· math.GR

Selfless reduced C^(*)-algebras of linear groups

Itamar Vigdorovich This is my paper
classification 🧮 math.OA math.DSmath.GR
keywords reducedlinearalgebraalgebrasgroupgroupsselflessamenable
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It is shown that the reduced C*-algebra of a nontrivial linear group $\Gamma<GL_{d}(k)$ with trivial amenable radical is selfless. Thus selflessness and simplicity coincide for reduced C*-algebras of linear groups. Similar results are obtained for twisted reduced group C*-algebra.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The Selfless Dichotomy

    math.OA 2026-06 unverdicted novelty 7.0

    Nonfaithful selfless C*-probability spaces are purely infinite and simple, so every selfless C*-algebra is either purely infinite or stably finite and hence pure.

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    math.OA 2026-04 unverdicted novelty 7.0

    A general family of selfless inclusions is established for reduced amalgamated free products of C*-algebras, with applications to new HNN extensions and selflessness for graph products over suitable graphs.