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 .

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Field (mathematics)
Quadratic forms
Quaternions