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Moscow Mathematical Journal

Volume 18, Issue 2, April–June 2018  pp. 321–347.

Exotic Matrix Models: the Albert Algebra and the Spin Factor

Authors:  Paul E. Gunnells (1)
Author institution:(1) Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305


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 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 𝕊 = 𝕊1,n , an algebra built on ℝn+1, and (ii) the Albert algebra 𝔸 of 3×3 Hermitian matrices over the octonions 𝕆. In this paper we investigate the matrix models attached to these remaining cases.

2010 Math. Subj. Class. Primary: 81T18, 16W10.

Keywords: Matrix models, octonions, Albert algebra, spin factor

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