Torsion subgroups of Whitehead groups of graded division algebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911834354745344 |
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| author | Khanh, Huynh Viet Khoa, Nguyen Duc Anh Khoi, Nguyen Dinh Anh |
| author_facet | Khanh, Huynh Viet Khoa, Nguyen Duc Anh Khoi, Nguyen Dinh Anh |
| contents | In this paper, we study the torsion subgroup, which is denoted by ${\rm TK}_1(E)$, of the Whitehead group $E^*/[E^*,E^*]$ of a graded division algebra $E$ which is finite dimensional over its center. In particular, we provide formulas for ${\rm TK}_1(E)$ in some special cases such as when $E$ is unramified, totally ramified or semiramified. Using the formulas, we are able to compute the group ${\rm TK}_1(D)$ of a valued division ring $D$, which is finite dimensional over a henselian center. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06801 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Torsion subgroups of Whitehead groups of graded division algebras Khanh, Huynh Viet Khoa, Nguyen Duc Anh Khoi, Nguyen Dinh Anh Rings and Algebras 16W60, 19B99, 16K20 In this paper, we study the torsion subgroup, which is denoted by ${\rm TK}_1(E)$, of the Whitehead group $E^*/[E^*,E^*]$ of a graded division algebra $E$ which is finite dimensional over its center. In particular, we provide formulas for ${\rm TK}_1(E)$ in some special cases such as when $E$ is unramified, totally ramified or semiramified. Using the formulas, we are able to compute the group ${\rm TK}_1(D)$ of a valued division ring $D$, which is finite dimensional over a henselian center. |
| title | Torsion subgroups of Whitehead groups of graded division algebras |
| topic | Rings and Algebras 16W60, 19B99, 16K20 |
| url | https://arxiv.org/abs/2404.06801 |