The low dimensional homology groups of the elementary group of degree two

2024/07/24 by Behrooz Mirzaii, Mirzaii, Behrooz, Elvis Torres Pérez +1 · 1 voice
Mathematics · #19D99 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT

paper · pdf · doi:10.48550/arxiv.2407.17632

openalex publication_date 2024/07/24 · arxiv published 2024/07/24 · openalex created_date 2025/10/10 · arxiv updated 2025/11/01 · openalex updated_date 2026/07/28

Abstract

In this article we study the first, the second and the third homology groups of the elementary group \textrmE₂(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∈ (A^×)² or |A^×/(A^×)²|≤ 4.

Discussions

• Behrooz Mirzaii, Elvis Torres P\'erez The low dimensional homology groups of the elementary group of rank two https://arxiv.org/abs/2407.17632 [bsky, 0 points, 0 comments]

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