Maximal tori of a general Lie algebra of Cartan type

M. I. Kuznetsov

Sbornik. Mathematics, Tome 188 (1997) no. 9, pp. 1317-1342

Résumé

A description is given of all maximal tori in the $p$-closure of a general Lie algebra $W(\mathscr F)$ of Cartan type over an algebraically closed field of characteristics of tori are found (dimension, algebra of invariants, weight functions root subspaces, the centralizer of a maximal torus) in terms of a defining system of functions of a maximal torus, and criteria are obtained for standartness and optimality of a maximal torus. A connection is established between the maximal tori in the $p$-closure and the Cartan subalgebras of $W(\mathscr F)$.

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