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arXiv · 2407.11608

Characters of diagonal products and Hilbert-Schmidt stability

Alon Dogon·Arie Levit·Itamar Vigdorovich
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Abstract

We initiate a quantitative study of Hilbert-Schmidt stability for infinitely presented groups through the novel notion of stability radius growth. We exhibit an uncountable family of Hilbert-Schmidt stable amenable groups with arbitrarily large such growth. In particular, this answers a question of Lubotzky. Our approach is based on the character-theoretic stability criterion of Hadwin and Shulman. We classify the characters of alternating and elementary enrichments as well as diagonal products, including the classical family of B.H. Neumann groups.

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Alon Dogon, Arie Levit, Itamar Vigdorovich. 2024-07-16. Characters of diagonal products and Hilbert-Schmidt stability. https://arxiv.org/abs/2407.11608

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