Quaternion algebras over elliptic curves

All composition algebras of rank 2 and 4 over elliptic curves are enumerated and partly classified, and examples of octonion algebras are constructed using the generalized Cayley-Dickson doubling process. The underlying field is assumed to be perfect, and of characteristic not two. Some applications are given.

Appeared in Comm. Algebra 26 (1998), 4357--4373.

S. Pumpluen <susanne.pumpluen@mathematik.uni-regensburg.de>