Deformations of $W_1(n) \otimes A$ and modular semisimple Lie algebras with a solvable maximal subalgebra

Details Deformations of $W_1(n) \otimes A$ and modular semisimple Lie algebras with a solvable maximal subalgebra Deformations of $W_1(n) \otimes A$ and modular semisimple Lie algebras with a solvable maximal subalgebra

2002-03-30

arxiv.org/abs/math/0204004v7

J. Algebra 268 (2003), 603-635

Mathematics

Rings and Algebras

v7: minor English and bibliographic corrections

Scientific paper

10.1016/S0021-8693(03)00295-3

In one of his last papers, Boris Weisfeiler proved that if modular semisimple Lie algebra possesses a solvable maximal subalgebra which defines in it a long filtration, then associated graded algebra is isomorphic to one constructed from the Zassenhaus algebra tensored with the divided powers algebra. We completely determine such class of algebras, calculating in process low-dimensional cohomology groups of Zassenhaus algebra tensored with any associative commutative algebra.

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