Quaternionic structure

In mathematics, a quaternionic structure or -structure is an axiomatic system that abstracts the concept of a quaternion algebra over a field.
A "quaternionic structure" is a triple where is an elementary abelian group of exponent with a distinguished element , is a pointed set with distinguished element , and is a symmetric surjection satisfying axioms
Every field gives rise to a -structure by taking to be , the set of Brauer classes of quaternion algebras in the Brauer group of with the split quaternion algebra as distinguished element and the quaternion algebra .