Questions tagged [jordan-algebras]

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 Neuman, 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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29
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1answer
3k views

What is about nonassociative geometry?

At the end of a conference given by Alain Connes in 2000 (here is a video in French), a member of the audience asked a question. I transcribed and translated it for you below: Audience: You showed ...
2
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2answers
508 views

polarization/linearization as in jordan forms

I am new to this branch of math, so bear with me. This question started when reading Kevin McCrimmon's "A Taste of Jordan Algebras" It talks about polarization and gives a general description. ...
13
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1answer
395 views

Are there nice isomorphisms $\operatorname{S}^2(k^n)\cong\Lambda^2(k^{n+1})$?

This might be forced to migrate to math.SE but let me still risk it. The spaces $\operatorname{S}^2(k^n)$ and $\Lambda^2(k^{n+1})$ from the title have equal dimensions. Is there a natural isomorphism ...