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Regular Cartan subalgebras and nilpotent elements in restricted Lie algebras. (Russian) Zbl 0691.17007

In Lie p-algebras the author considers elementary transformations which are generalizations of Winter’s exponential maps [D. J. Winter, Acta Math. 123, 69-81 (1969; Zbl 0181.046)]. It is proved that any two Cartan subalgebras being centralizers of tori of maximal dimension could be transferred one into another by means of a finite number of elementary transformations. The minimal p-polynomial of the general element of the Lie p-algebra is given. A novel proof of the result obtained by E. M. Friedlander and B. J. Parshall [Invent. Math. 86, 553-562 (1986; Zbl 0626.17010)] on the connectivity of the projective variety of nilpotent elements in a Lie p-algebra is given. The proof is based on the classification of Lie algebras without strong degeneration and does not make use of cohomology techniques.
Reviewer: M.Kuznetsov

MSC:

17B50 Modular Lie (super)algebras
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
17B05 Structure theory for Lie algebras and superalgebras
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