# 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.

**2**

**0**answers

### Lie Groups and Lie algebras related to Jordan algebras

**1**

**0**answers

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

**0**

**0**answers

### Explicit isomorphism between two Jordan algebras

**4**

**1**answer

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

**1**

**1**answer

### Relating classic spectral decomposition with Euclidean Jordan algebras

**1**

**0**answers

### Good source for Jordan Fréchet algebras

**3**

**0**answers

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

**6**

**0**answers

### Formally real non-Jordan algebras

**7**

**1**answer

### Jordan algebra identities

**3**

**2**answers

### Jordan isomorphisms of type I von Neumann algebras

**3**

**0**answers

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

**2**

**0**answers

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

**1**

**2**answers

### Determinants in Jordan algebras of Euclidean type

**13**

**1**answer

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

**6**

**0**answers

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

**2**

**0**answers

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

**0**

**0**answers

### Notion of trace in a Jordan algebra

**5**

**1**answer

### Looking for Severi varieties

**5**

**1**answer

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

**1**

**1**answer

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

**2**

**0**answers

### Automorphism groups of symmetric cones

**1**

**1**answer

### Square of Pierce 1/2 elements

**5**

**0**answers

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

**29**

**1**answer

### What is about nonassociative geometry?

**2**

**2**answers

### polarization/linearization as in jordan forms

**9**

**3**answers

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

**3**

**1**answer

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

**6**

**2**answers