# 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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### Nonassociative algebras closed under $\sqrt{\ }$?

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### Explicit isomorphism between two Jordan algebras

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### Left- (right-) multiplications of an algebra that are derivations

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### Relating classic spectral decomposition with Euclidean Jordan algebras

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### Good source for Jordan Fréchet algebras

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### Alfsen Shultz theorem-the space of states of $C^*$-algebra depends only on Jordan structure

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### Formally real non-Jordan algebras

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### Jordan algebra identities

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### Jordan isomorphisms of type I von Neumann algebras

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### Is there a unique way to define an Euclidean Jordan Algebra as the product of two simple Euclidean Jordan Algebras?

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### Automorphism group of formally real Jordan algebras of hermitian matrices

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### Determinants in Jordan algebras of Euclidean type

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

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### A characterisation of certain $C^*$-algebras

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### Is -1 a sum of Hermitian squares in associative *-envelopes of formally real Jordan algebras?

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### Notion of trace in a Jordan algebra

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### Looking for Severi varieties

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### Is the generated subalgebra of a subset of pairwise operator-commuting element in a JB-algebra associative?

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### how to write down comatrix of the exceptional Jordan algebra

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### Automorphism groups of symmetric cones

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### Square of Pierce 1/2 elements

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### Reference request: The relationship between norm and trace forms on an Albert algebra

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### What is about nonassociative geometry?

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### polarization/linearization as in jordan forms

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### Algebraic axiomatization for AB+BA^T operation on matrices

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### ABA-product of matrices and length of chains of principal inner ideals

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