In abstract algebra, a Jordan algebra is an (not necessarily associative) algebra over a field whose multiplication satisfies the following axioms:
- (commutative law)
- (Jordan identity).
The product of two elements x and y in a Jordan algebra is also denoted x ∘ y, particularly to avoid confusion with the product of a related associative algebra. The axioms imply that a Jordan algebra is power-associative and satisfies the following generalization of the Jordan identity: for all positive integers m and n.
Jordan algebras were first introduced by Pascual Jordan (1933) to formalize the notion of an algebra of observables in quantum mechanics. They were originally called "r-number systems", but were renamed "Jordan algebras" by Albert (1946), who began the systematic study of general Jordan algebras.
Read more about Jordan Algebra: Special Jordan Algebras, Examples, Derivations and Structure Algebra, Formally Real Jordan Algebras, Peirce Decomposition
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