Topological and differentiable aspects of Clifford semigroups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917436675063808 |
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| author | Bonzio, Stefano Loi, Andrea Zecchini, Giuseppe |
| author_facet | Bonzio, Stefano Loi, Andrea Zecchini, Giuseppe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23326 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological and differentiable aspects of Clifford semigroups Bonzio, Stefano Loi, Andrea Zecchini, Giuseppe General Topology Commutative Algebra Group Theory 22A15, 20M18 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. |
| title | Topological and differentiable aspects of Clifford semigroups |
| topic | General Topology Commutative Algebra Group Theory 22A15, 20M18 |
| url | https://arxiv.org/abs/2604.23326 |