Geodesic
Maximal tori of a~general Lie algebra of Cartan type
Sbornik. Mathematics, Tome 188 (1997) no. 9, pp. 1317-1342

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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 $W(\mathscr F)$. 
@article{SM_1997_188_9_a3,
     author = {M. I. Kuznetsov},
     title = {Maximal tori of a~general {Lie} algebra of {Cartan} type},
     journal = {Sbornik. Mathematics},
     pages = {1317--1342},
     publisher = {mathdoc},
     volume = {188},
     number = {9},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_9_a3/}
}
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M. I. Kuznetsov. Maximal tori of a~general Lie algebra of Cartan type. Sbornik. Mathematics, Tome 188 (1997) no. 9, pp. 1317-1342. http://geodesic.mathdoc.fr/item/SM_1997_188_9_a3/