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 [10.1007/s00031-015-9362-5].

Restricted Lie algebras with maximal 0-PIM

WEIGEL, THOMAS STEFAN
2016

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 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.
Articolo in rivista - Articolo scientifico
Restricted Lie algebras, p-character, reduced universal enveloping algebra, projective cover, projective indecomposable module, induced module, maximal 0-PIM, torus, solvable Lie algebra, number of irreducible modules
English
377
398
22
Feldvoss, J., Siciliano, S., & Weigel, T. (2016). Restricted Lie algebras with maximal 0-PIM. TRANSFORMATION GROUPS, 21(2), 377-398 [10.1007/s00031-015-9362-5].
Feldvoss, J; Siciliano, S; Weigel, T
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/139077
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