Protori and Torsion-Free Abelian Groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866912295588724736 |
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| author | Lewis, Wayne |
| author_facet | Lewis, Wayne |
| contents | The Resolution Theorem for Compact Abelian Groups is applied to show that the profinite subgroups of a finite-dimensional compact connected abelian group (protorus) which induce tori quotients comprise a lattice under intersection (meet) and $+$ (join), facilitating a proof of the existence of a universal resolution. A finite rank torsion-free abelian group $X$ is algebraically isomorphic to a canonical dense subgroup $X_G$ of its Pontryagin dual $G$. A morphism between protori lifts to a product morphism between the universal covers, so morphisms in the category can be studied as pairs of maps: homomorphisms between finitely generated profinite abelian groups and linear maps between finite-dimensional real vector spaces. A concept of non-Archimedean dimension is introduced which acts a useful invariant for classifying protori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_08022 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Protori and Torsion-Free Abelian Groups Lewis, Wayne Group Theory 20K15, 20K20, 20K25, 22B05, 22C05, 22D35 The Resolution Theorem for Compact Abelian Groups is applied to show that the profinite subgroups of a finite-dimensional compact connected abelian group (protorus) which induce tori quotients comprise a lattice under intersection (meet) and $+$ (join), facilitating a proof of the existence of a universal resolution. A finite rank torsion-free abelian group $X$ is algebraically isomorphic to a canonical dense subgroup $X_G$ of its Pontryagin dual $G$. A morphism between protori lifts to a product morphism between the universal covers, so morphisms in the category can be studied as pairs of maps: homomorphisms between finitely generated profinite abelian groups and linear maps between finite-dimensional real vector spaces. A concept of non-Archimedean dimension is introduced which acts a useful invariant for classifying protori. |
| title | Protori and Torsion-Free Abelian Groups |
| topic | Group Theory 20K15, 20K20, 20K25, 22B05, 22C05, 22D35 |
| url | https://arxiv.org/abs/1903.08022 |