$S_4$-symmetry on the Tits construction of exceptional Lie algebras and superalgebras
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The classical Tits construction provides models of the exceptional
simple Lie algebras in terms of a unital composition algebra and a
degree three simple Jordan algebra. A couple of actions of the
symmetric group $S_4$ on this construction are given. By means of
these actions, the models provided by the Tits construction are
related to models of the exceptional Lie algebras obtained from two
different types of structurable algebras. Some models of exceptional
Lie superalgebras are discussed too.
simple Lie algebras in terms of a unital composition algebra and a
degree three simple Jordan algebra. A couple of actions of the
symmetric group $S_4$ on this construction are given. By means of
these actions, the models provided by the Tits construction are
related to models of the exceptional Lie algebras obtained from two
different types of structurable algebras. Some models of exceptional
Lie superalgebras are discussed too.
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Com citar
Elduque, A.; and Okubo, S. “$S_4$-symmetry on the Tits construction of exceptional Lie algebras and superalgebras”. Publicacions Matemàtiques, vol.VOL 52, no. 2, pp. 315-46, https://raco.cat/index.php/PublicacionsMatematiques/article/view/113436.