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Mosc. Math. J., 2018, Volume 18, Number 2, Pages 321–347 (Mi mmj674)  

Exotic matrix models: the albert Algebra and the spin factor

Paul E. Gunnells

Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305

Abstract: The matrix models attached to real symmetric matrices and the complex/quaternionic Hermitian matrices have been studied by many authors. These models correspond to three of the simple formally real Jordan algebras over $\mathbb R$. Such algebras were classified by Jordan, von Neumann, and Wigner in the 30s, and apart from these three there are two others: (i) the spin factor $\mathbb S=\mathbb S_{1,n}$, an algebra built on $\mathbb R^{n+1}$, and (ii) the Albert algebra $\mathbb A$ of $3\times3$ Hermitian matrices over the octonions $\mathbb O$. In this paper we investigate the matrix models attached to these remaining cases.

Key words and phrases: matrix models, octonions, Albert algebra, spin factor.

Full text: http://www.mathjournals.org/.../2018-018-002-005.html
References: PDF file   HTML file

Document Type: Article
MSC: 81T18, 16W10
Language: English

Citation: Paul E. Gunnells, “Exotic matrix models: the albert Algebra and the spin factor”, Mosc. Math. J., 18:2 (2018), 321–347

Citation in format AMSBIB
\Bibitem{Gun18}
\by Paul~E.~Gunnells
\paper Exotic matrix models: the albert Algebra and the spin factor
\jour Mosc. Math.~J.
\yr 2018
\vol 18
\issue 2
\pages 321--347
\mathnet{http://mi.mathnet.ru/mmj674}


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