RESTRICTED LIE ALGEBRAS WITH MAXIMAL 0-PIM |
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Authors: | Email author" target="_blank">J?RG?FELDVOSSEmail author SALVATORE?SICILIANO THOMAS?WEIGEL |
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Institution: | 1.Department of Mathematics and Statistics,University of South Alabama,Mobile,USA;2.Dipartimento di Matematica e Fisica “Ennio De Giorgi”,Università del Salento,Lecce,Italy;3.Dipartimento di Matematica e Applicazioni,Università degli Studi di,Milano,Italy |
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Abstract: | In this paper it is shown that the projective cover of the trivial irreducible module of a finite-dimensional solvable restricted Lie algebra is induced from the one dimensional trivial module of a maximal torus. As a consequence, the number of the isomorphism classes of irreducible modules with a fixed p-character for a finite-dimensional solvable restricted Lie algebra L is bounded above by p MT(L), where MT(L) denotes the maximal dimension of a torus in L. Finally, it is proved that in characteristic p > 3 the projective cover of the trivial irreducible L-module is induced from the one-dimensional trivial module of a torus of maximal dimension, only if L is solvable. |
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