The low dimensional homology groups of the elementary group of degree two
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909881109315584 |
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| author | Mirzaii, Behrooz Pérez, Elvis Torres |
| author_facet | Mirzaii, Behrooz Pérez, Elvis Torres |
| contents | In this article we study the first, the second and the third homology groups of the elementary group $\textrm{E}_2(A)$, where $A$ is a commutative ring. In particular, we prove a refined Bloch-Wigner type exact sequence over a semilocal ring (with some mild restriction on its residue fields) such that $-1\in (A^{\times})^2$ or $|A^{\times}/(A^{\times})^2|\leq 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17632 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The low dimensional homology groups of the elementary group of degree two Mirzaii, Behrooz Pérez, Elvis Torres K-Theory and Homology 19D99 In this article we study the first, the second and the third homology groups of the elementary group $\textrm{E}_2(A)$, where $A$ is a commutative ring. In particular, we prove a refined Bloch-Wigner type exact sequence over a semilocal ring (with some mild restriction on its residue fields) such that $-1\in (A^{\times})^2$ or $|A^{\times}/(A^{\times})^2|\leq 4$. |
| title | The low dimensional homology groups of the elementary group of degree two |
| topic | K-Theory and Homology 19D99 |
| url | https://arxiv.org/abs/2407.17632 |