Generalized restricted Lie algebras and representations of the Zassenhaus algebra

摘要

Let F be a field of characteristic p > 0, L a generalized restricted Lie algebra over F, and P(L) the primitive p-envelope of L. A close relation between L-representations and P(L)-representations is established. In particular, the irreducible kappa-reduced modules of L for any kappa is an element of L* coincide with the irreducible <(kappa)over bar>(0)-reduced modules of P(L), where <(kappa)over bar>(0) is an element of P(L)* is a trivial extension of kappa. From this result, the determination of all irreducible representations of the Zassenhaus algebra is completed, and the dimensions of the corresponding modules are also given. (C) 1998 Academic Press. [References: 29]