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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A non-restricted counterexample to the first Kac–Weisfeiler conjecture
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by Lewis Topley PDF
Proc. Amer. Math. Soc. 145 (2017), 1937-1942 Request permission

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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Additional Information
  • Lewis Topley
  • Affiliation: Dipartimento di Matematica, Universita di Padova, via Trieste 63, Padova, Italy
  • MR Author ID: 1048635
  • Email: lewis@unipd.it
  • 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
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 1937-1942
  • MSC (2010): Primary 17B50
  • DOI: https://doi.org/10.1090/proc/13362
  • MathSciNet review: 3611310