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Questions tagged [jordan-algebras]

This tag is for questions related to Jordan algebras. They constitute one of the first classes of non-associative algebras.

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Recommended books on JB-algebra

I want to find a self-contained book on JB-algebras, just like Murphy's book on C*-algebra. Any suggestion?
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Analogy of Exponential Map for Jordan Algebras

Today I gave a talk about this paper that constructs a Jordan algebra (more precisely, a JB algebra) to model (bounded) physical observables. It cites this paper, that proves that every JB algebra $A$ ...
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When is a homogeneous cone a Jordan Banach algebra?

A (closed) positive cone $C$ in a vector space $V$ is called homogeneous if for for all $a$ and $b$ in the interior of $C$ there exists an order isomorphism $\Phi: V\rightarrow V$ (i.e. a linear ...
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Mirror symmetries of the Albert algebra

A simple Euclidean Jordan algebra (i.e. a factor) is either a spin-factor, the matrices over the reals/complex-numbers/quaternions or the exceptional Albert algebra of 3x3 octonian matrices. My ...
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Is the quadratic form of a Euclidean Jordan Algebra positive?

A Jordan Algebra $(V,*)$ is an algebra with a commutative (not associative) multiplication operator $*$ that satisfies the Jordan identity: $(x*y)*(x*x) = x*(y*(x*x))$. The positive cone consists of ...
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Complex integration using a suitable contour

$$\int_{-\infty}^{\infty} \frac{x\sin x}{x^2 +4} \ dx$$ Can someone show me how to evaluate this integral by integrating around a suitable contour. I've seen similar questions however I think you ...
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Algebra Symbols $\mathfrak h$ and $\mathfrak{so}$

What do these symbols mean in algebra? I found them as follows: $$\mathfrak h_3(\Bbb O(\Bbb Z_p))$$ $$\mathfrak{so}(\Bbb O)\oplus\Bbb O^3$$
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What is meant by $A^{+}$ and $A^{-}$ in algebra? [closed]

What is meant by $A^{+}$ and $A^{-}$ in algebra? I read it in Jordan Algebra $A^+$
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Jordan form from the minimal polynomial $m_A$

Let the matrix \begin{equation} A=\begin{bmatrix} 1 & 0 & -1 \\ 4 & 3 & 2 \\\ 2 & 1 & 1 \end{bmatrix}. \end{equation} So far I found the characteristic polynomial $C_A(x)=(x-...
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Proof-Explanation, why does this imply 1-1

Theorem : Let T be a linear operator on a vector space V and let $\lambda$ be an eigenvalue of T. Then : For any scalar $\mu \not = \lambda$, the restriction of T - $\mu$I to $K_\lambda$ is one - to -...
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What was the genesis of Hua's identity?

Many resources I have read prove Hua's identity more-or-less mechanically. I have seen there is more than one raison d'être for Hua's identity: e.g. its connection to the fundamental theorem of ...