A non-restricted counterexample to the first Kac-Weisfeiler conjecture
Author:
Lewis Topley
Journal:
Proc. Amer. Math. Soc. 145 (2017), 1937-1942
MSC (2010):
Primary 17B50
DOI:
https://doi.org/10.1090/proc/13362
Published electronically:
October 27, 2016
MathSciNet review:
3611310
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Abstract | References | Similar Articles | Additional Information
Abstract: 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.
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-algebras, Funkcional. Anal. i Priložen. 5 (1971), no. 2, 28-36 (Russian). Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 17B50
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Additional Information
Lewis Topley
Affiliation:
Dipartimento di Matematica, Universita di Padova, via Trieste 63, Padova, Italy
Email:
lewis@unipd.it
DOI:
https://doi.org/10.1090/proc/13362
Keywords:
Modular Lie algebras,
irreducible representations
Received by editor(s):
May 23, 2016
Received by editor(s) in revised form:
June 28, 2016, and July 4, 2016
Published electronically:
October 27, 2016
Communicated by:
Kailash C. Misra
Article copyright:
© Copyright 2016
American Mathematical Society
