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Jordan algebra
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===Hermitian Jordan algebras=== If (''A'', ''σ'') is an associative algebra with an [[involution (mathematics)|involution]] ''σ'', then if ''σ''(''x'') = ''x'' and ''σ''(''y'') = ''y'' it follows that <math display="inline">\sigma(xy + yx) = xy + yx.</math> Thus the set of all elements fixed by the involution (sometimes called the ''hermitian'' elements) form a subalgebra of ''A''<sup>+</sup>, which is sometimes denoted H(''A'',''σ'').
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