# Norms and determinants of quaternionic line bundles

Research paper by Johannes Cleven

Indexed on: 01 Jul '98Published on: 01 Jul '98Published in: Archiv der Mathematik

#### Abstract

We investigate the relationship between the determinants det (P) and norms N ( P ) of right modules P of rank one over associative composition algebras C. We show: $${\rm det} (P) \cong N(P) \otimes N(P)$$ if C is a quaternion algebra, and $${\rm det}\,(P) \cong N(P) \otimes {\rm det}\, (C)$$ if C is a quadratic étale algebra.