\(S_4\)-symmetry on the Tits construction of exceptional Lie algebras and superalgebras. (English) Zbl 1209.17010

This paper explores the two main models for exceptional Lie algebras, given by the now classical Tits construction [J. Tits, Nederl. Akad. Wet., Proc., Ser. A 65, 530–535 (1962; Zbl 0104.26002)] and the stucturable algebras [B. N. Allison, Math. Ann. 237, 133–156 (1978; Zbl 0368.17001)] respectively. The models are compared by means of the action of the symmetric group of four letters on the Lie algebras, as previously analyzed by the authors [ J. Algebra 307, No. 2, 864–890 (2007; Zbl 1172.17013)]. The procedure allows to obtain a characterization of Lie algebras with an \(S_{4}\) action with a unital coordinate algebra. The ansatz is also discussed in the case of Lie superalgebras.


17B25 Exceptional (super)algebras
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