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Irreducible representations of strongly solvable Lie algebras over a field of positive characteristic. (Russian) Zbl 0542.17004
Let L be a strongly solvable Lie algebra over an algebraically closed field of characteristic $$p>0$$. In this study of irreducible representations of such algebras the author is able to obtain a number of results which are valid even if L is not restricted. This is made possible in part by consideration of the Lie algebra of derivations of the form (ad x)$${}^{p^ k}$$, 0$$\leq k$$, $$x\in L$$. It is also shown that the structure of irreducible representations of L can be deduced from that of irreducible representations of a certain restricted Lie algebra into which L can be mapped by an injective homomorphism. The dimension of an irreducible module of weight $${\mathfrak z}$$ depends on the dimension of the stationary subalgebra of a certain linear functional $$\tilde {\mathfrak z}$$. A formula is obtained for the number of nonisomorphic representations of a strongly solvable restricted Lie algebra. The results are applied to describe certain irreducible representations of a maximal subalgebra of a Zassenhaus algebra.
Reviewer: G.Brown

##### MSC:
 17B50 Modular Lie (super)algebras 17B30 Solvable, nilpotent (super)algebras
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