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 pMT(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.
Feldvoss, J., Siciliano, S., & Weigel, T. (2016). Restricted Lie algebras with maximal 0-PIM. TRANSFORMATION GROUPS, 21(2), 377-398.
Citazione: | Feldvoss, J., Siciliano, S., & Weigel, T. (2016). Restricted Lie algebras with maximal 0-PIM. TRANSFORMATION GROUPS, 21(2), 377-398. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Presenza di un coautore afferente ad Istituzioni straniere: | Si |
Titolo: | Restricted Lie algebras with maximal 0-PIM |
Autori: | Feldvoss, J; Siciliano, S; Weigel, T |
Autori: | |
Data di pubblicazione: | 2016 |
Lingua: | English |
Rivista: | TRANSFORMATION GROUPS |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00031-015-9362-5 |
Appare nelle tipologie: | 01 - Articolo su rivista |
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