Topological and differentiable aspects of Clifford semigroups

Stefano Bonzio; Andrea Loi; Giuseppe Zecchini

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arXiv · 2604.23326

Topological and differentiable aspects of Clifford semigroups

Stefano Bonzio·Andrea Loi·Giuseppe Zecchini

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Abstract

This paper investigates the interplay between algebraic structure, topology, and differentiability in Clifford semigroups. The study is developed along three main themes. First, in the compact Hausdorff setting, we provide an explicit construction of a compatible metric for the Bowman topology. Second, we address Hilbert-fifth-type questions by establishing criteria under which the maximal subgroups are forced to be Lie groups. Finally, we prove a structural rigidity theorem: $C^1$-regularity at the idempotents implies that the idempotent semilattice is discrete.

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Stefano Bonzio, Andrea Loi, Giuseppe Zecchini. 2026-04-25. Topological and differentiable aspects of Clifford semigroups. https://arxiv.org/abs/2604.23326

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