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December 2011 $E_7$ groups from octonionic magic square
Sergio L. Cacciatori, Francesco Dalla Piazza, Antonio Scotti
Adv. Theor. Math. Phys. 15(6): 1605-1654 (December 2011).

Abstract

In this paper, we continue our program, started in Euler angles for $G(2)$, of building up explicit generalized Euler angle parameterizations for all exceptional compact Lie groups. Here we solve the problem for $E_7$, by first providing explicit matrix realizations of the Tits construction of a Magic Square product between the exceptional octonionic algebra $\mathfrak{J}$ and the quaternionic algebra $\mathbb{H}$, both in the adjoint and the 56-dimensional representations. Then, we provide the Euler parametrization of $E_7$ starting from its maximal subgroup $U = (E_6 \times U(1))/\mathbb{Z}_3$. Next, we give the constructions for all the other maximal compact subgroups.

Citation

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Sergio L. Cacciatori. Francesco Dalla Piazza. Antonio Scotti. "$E_7$ groups from octonionic magic square." Adv. Theor. Math. Phys. 15 (6) 1605 - 1654, December 2011.

Information

Published: December 2011
First available in Project Euclid: 12 December 2012

zbMATH: 1267.81191
MathSciNet: MR2989810

Rights: Copyright © 2011 International Press of Boston

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Vol.15 • No. 6 • December 2011
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