About: Noncommutative Jordan algebra

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In algebra, a noncommutative Jordan algebra is an algebra, usually over a field of characteristic not 2, such that the four operations of left and right multiplication by x and x2 all commute with each other. Examples include associative algebras and Jordan algebras. Over fields of characteristic not 2, noncommutative Jordan algebras are the same as flexible Jordan-admissible algebras, where a Jordan-admissible algebra – introduced by Albert and named after Pascual Jordan – is a (possibly non-associative) algebra that becomes a Jordan algebra under the product a ∘ b = ab + ba.

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  • In algebra, a noncommutative Jordan algebra is an algebra, usually over a field of characteristic not 2, such that the four operations of left and right multiplication by x and x2 all commute with each other. Examples include associative algebras and Jordan algebras. Over fields of characteristic not 2, noncommutative Jordan algebras are the same as flexible Jordan-admissible algebras, where a Jordan-admissible algebra – introduced by Albert and named after Pascual Jordan – is a (possibly non-associative) algebra that becomes a Jordan algebra under the product a ∘ b = ab + ba. (en)
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  • In algebra, a noncommutative Jordan algebra is an algebra, usually over a field of characteristic not 2, such that the four operations of left and right multiplication by x and x2 all commute with each other. Examples include associative algebras and Jordan algebras. Over fields of characteristic not 2, noncommutative Jordan algebras are the same as flexible Jordan-admissible algebras, where a Jordan-admissible algebra – introduced by Albert and named after Pascual Jordan – is a (possibly non-associative) algebra that becomes a Jordan algebra under the product a ∘ b = ab + ba. (en)
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  • Noncommutative Jordan algebra (en)
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