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- Quaternionic_structure abstract "In mathematics, a quaternionic structure or Q-structure is an axiomatic system that abstracts the concept of a quaternion algebra over a field.A quaternionic structure is a triple (G,Q,q) where G is an elementary abelian group of exponent 2 with a distinguished element −1, Q is a pointed set with distinguished element 1, and q is a symmetric surjection from G×G → Q satisfying axioms q(a,(−1)a) = 1; q(a,b) = q(a,c) ⇔ q(a,bc) = 1; q(a,b) = q(c,d) ⇒ ∃x . q(a,b) = q(a,x), q(c,d) = q(c,x).Every field F gives rise to a Q-structure by taking G to be F∗/F∗2, Q the set of Brauer classes of quaternion algebras in the Brauer group of F with the split quaternion algebra as distinguished element and q(a,b) the quaternion algebra (a,b)F.".
- Quaternionic_structure wikiPageID "39227817".
- Quaternionic_structure wikiPageRevisionID "575796587".
- Quaternionic_structure subject Category:Field_theory.
- Quaternionic_structure subject Category:Quadratic_forms.
- Quaternionic_structure subject Category:Quaternions.
- Quaternionic_structure comment "In mathematics, a quaternionic structure or Q-structure is an axiomatic system that abstracts the concept of a quaternion algebra over a field.A quaternionic structure is a triple (G,Q,q) where G is an elementary abelian group of exponent 2 with a distinguished element −1, Q is a pointed set with distinguished element 1, and q is a symmetric surjection from G×G → Q satisfying axioms q(a,(−1)a) = 1; q(a,b) = q(a,c) ⇔ q(a,bc) = 1; q(a,b) = q(c,d) ⇒ ∃x .".
- Quaternionic_structure label "Quaternionic structure".
- Quaternionic_structure sameAs m.0t_frsy.
- Quaternionic_structure sameAs Q17067274.
- Quaternionic_structure sameAs Q17067274.
- Quaternionic_structure wasDerivedFrom Quaternionic_structure?oldid=575796587.
- Quaternionic_structure isPrimaryTopicOf Quaternionic_structure.