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Results tagged with jordan-algebras
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user 174691
A Jordan algebra is an algebra with multiplication satisfying two axioms (J1) xy=yx (J2) (xxy)x=xx(yx). They were defined in 1934 by Jordan, von Neumann, and Wigner seeking a better formalism for quantum mechanics. In 1966 McCrimmon proposed to analyze instead the operator Ux(y)=xyx, which lead to a notion of quadratic Jordan algebras. Three axioms (Q1, Q2, Q3) of these objects can be found below.
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Relating classic spectral decomposition with Euclidean Jordan algebras
When $x$ is idempotent, the operator $L_x$ has three eigenvalues, $0$, $1$ and $\frac12$. This leads to a decomposition of the space into three subspaces, known as the Peirce decomposition. Now for an …
- 136
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Is the generated subalgebra of a subset of pairwise operator-commuting element in a JB-algeb...
Yes, this is true. I couldn't find any proof of the statement you quote in the article, and even after emailing the authors I didn't get any wiser, so I decided to work out the details myself, see my …
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