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π SIMILAR VOLUMES
Leibniz representation of the Lie algebra α is a vector space M equipped with Ε½ .w x w x two actions left and right α, α : α m M Βͺ M and α, α : M m α Βͺ M which satisfy the relations \* Partially supported by Grant INTAS-93-2618. 414
We present an explicit description of the α -support supp M of any irreducible α -locally finite α-module M, where α is any finite-dimensional Lie algebra and α is an arbitrary nilpotent Lie subalgebra of α. If α contains a Cartan subalgebra of the semi-simple part of α, we reformulate the description
Let F be a field of characteristic p ) 0, L a generalized restricted Lie algebra Ε½ . over F, and P L the primitive p-envelope of L. A close relation between Ε½ . L-representations and P L -representations is established. In particular, the irreducible -reduced modules of L for any g L\* coincide with
In a recent paper by Xu, some simple Lie algebras of generalized Cartan type were constructed, using the mixtures of grading operators and down-grading operators. Among them are the simple Lie algebras of generalized Witt type, which are in general nongraded and have no torus. In this paper, some re