Hyperbolic Unit Groups and Quaternion Algebras

2007/09/13 by S. O. Juriaans, Inder Bir S. Passi, Juriaans, S. O. +3
Mathematics · #16S34 #16U60 #20F67 #Algebraic and Geometric Analysis #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0709.2161

openalex publication_date 2007/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct units in a non-split quaternion algebra over R.

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