On the connections between the low dimensional homology groups of $\textrm{SL}_2$ and $\textrm{PSL}_2$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917698641854464 |
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| author | Mirzaii, Behrooz Pérez, Elvis Torres |
| author_facet | Mirzaii, Behrooz Pérez, Elvis Torres |
| contents | In this article we study the low dimensional homology groups of the special linear group $\textrm{SL}_2(A)$ and the projective special linear group $\textrm{PSL}_2(A)$, $A$ a domain, through the natural surjective map $\textrm{SL}_2(A) \to \textrm{PSL}_2(A)$. In particular, we study the connection of the first, the second and the third homology groups of these groups over euclidean domains $\mathbb{Z}[\frac{1}{m}]$, $m$ a square free integer, and local domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08074 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the connections between the low dimensional homology groups of $\textrm{SL}_2$ and $\textrm{PSL}_2$ Mirzaii, Behrooz Pérez, Elvis Torres K-Theory and Homology In this article we study the low dimensional homology groups of the special linear group $\textrm{SL}_2(A)$ and the projective special linear group $\textrm{PSL}_2(A)$, $A$ a domain, through the natural surjective map $\textrm{SL}_2(A) \to \textrm{PSL}_2(A)$. In particular, we study the connection of the first, the second and the third homology groups of these groups over euclidean domains $\mathbb{Z}[\frac{1}{m}]$, $m$ a square free integer, and local domains. |
| title | On the connections between the low dimensional homology groups of $\textrm{SL}_2$ and $\textrm{PSL}_2$ |
| topic | K-Theory and Homology |
| url | https://arxiv.org/abs/2402.08074 |