The low dimensional homology of projective linear group of rank two

2024/05/14 by Behrooz Mirzaii, Mirzaii, Behrooz, Elvis Torres Pérez +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2405.08950

openalex publication_date 2024/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study the low dimensional homology of the projective linear group \textrmPGL₂(A) over a commutative ring A. In particular, we prove a Bloch-Wigner type exact sequence over local domains. As applications we prove that H₂(\textrmPGL₂(A),ℤ[(1)/(2)])≃ K₂(A)[(1)/(2)] and H₃(\textrmPGL₂(A),ℤ[(1)/(2)])≃ K₃^\textrmind(A)[(1)/(2)] provided |A/m_A|≠ 2,3,4,8.

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