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Representations of Lie algebras in prime characteristic

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Representation Theories and Algebraic Geometry

Part of the book series: Nato ASI Series ((ASIC,volume 514))

Abstract

The aim of these lectures is to give a survey on the representation theory of Lie algebras of reductive groups in prime characteristic. This theory is quite different from the corresponding theory in characteristic O. For example, in prime characteristic all simple modules are finite dimensional. On the other hand, there is in most cases no classification of these simple modules. There has been major progress in this area in the last few years, mostly related to Premet’s proof (from 1995) of the Kac-Weisfeiler conjecture (from 1971).

The first four sections discuss the representation theory of general (restricted) Lie algebras in prime characteristic as well as some special aspects in the cases of unipotent and solvable Lie algebras. The rest of the text then deals more specifically with Lie algebras of reductive groups.

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Authors and Affiliations

  1. Matematisk Institut Aarhus, Universitet Ny Munkegade, DK-8000, Aarhus C, Denmark

    Jens Carsten Jantzen

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  1. Jens Carsten Jantzen
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  1. Department of Mathematics and Statistics, University of Montreal, Montreal, Canada

    Abraham Broer , A. Daigneault  & Gert Sabidussi ,  & 

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Jantzen, J.C. (1998). Representations of Lie algebras in prime characteristic. In: Broer, A., Daigneault, A., Sabidussi, G. (eds) Representation Theories and Algebraic Geometry. Nato ASI Series, vol 514. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9131-7_5

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  • DOI: https://doi.org/10.1007/978-94-015-9131-7_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5075-5

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