A non-restricted counterexample to the first Kac–Weisfeiler conjecture
Copyright policy )A non-restricted counterexample to the first Kac–Weisfeiler conjecture
In 1971 Kac and Weisfeiler made two important conjectures regarding the representation theory of restricted Lie algebras over fields of positive characteristic. The first of these predicts the maximal dimension of the simple modules, and can be stated without the hypothesis that the Lie algebra is restricted. In this short article we construct the first example of a non-restricted Lie algebra for which the prediction of the first Kac--Weisfeiler conjecture fails. Our method is to present pairs of Lie algebras which have isomorphic enveloping algebras but distinct indexes.
A few typos corrected; 5 pages
- University of Padua Italy
Modular Lie (super)algebras, Rings and Algebras (math.RA), FOS: Mathematics, modular Lie algebras, irreducible representations, Mathematics - Rings and Algebras, Representation Theory (math.RT), Universal enveloping (super)algebras, Mathematics - Representation Theory
Modular Lie (super)algebras, Rings and Algebras (math.RA), FOS: Mathematics, modular Lie algebras, irreducible representations, Mathematics - Rings and Algebras, Representation Theory (math.RT), Universal enveloping (super)algebras, Mathematics - Representation Theory
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