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- W2000772168 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." @default.
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- W2000772168 date "2011-01-01" @default.
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- W2000772168 title "$E_7$ groups from octonionic magic square" @default.
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- W2000772168 doi "https://doi.org/10.4310/atmp.2011.v15.n6.a2" @default.
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