Lie algebras of type 𝐵𝐶₁

Allison, B. N.

doi:10.1090/S0002-9947-1976-0432724-5

Lie algebras of type $BC_{1}$
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Trans. Amer. Math. Soc. 224 (1976), 75-86 Request permission

Abstract:

Let L be a central simple Lie algebra of type $B{C_1}$ with highest root space of dimension greater than one over a field of characteristic zero. It is shown that either L is isomorphic to the simple Lie algebra associated with a skew hermitian form of index one or L can be constructed from the tensor product of two composition algebras. This result is obtained by completing the description (begun in [3]) of the corresponding class of ternary algebras.

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