On the connections between the low dimensional homology groups of \textrmSL₂ and \textrmPSL₂

2024/02/12 by Mirzaii, Behrooz, Pérez, Elvis Torres · 1 citation
#FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2402.08074

Abstract

In this article we study the low dimensional homology groups of the special linear group \textrmSL₂(A) and the projective special linear group \textrmPSL₂(A), A a domain, through the natural surjective map \textrmSL₂(A) → \textrmPSL₂(A). In particular, we study the connection of the first, the second and the third homology groups of these groups over euclidean domains ℤ[(1)/(m)], m a square free integer, and local domains.

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• Schur multiplier of SL₂ over finite commutative rings

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