# 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

**Summary: **

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 = 𝕊_{1,n }, an algebra built on ℝ^{n+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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