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Varieties of Elementary Subalgebras of Maximal Dimension for Modular Lie Algebras

  • Julia Pevtsova
  • Jim Stark
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 242)

Abstract

Motivated by questions in modular representation theory, Carlson, Friedlander, and the first author introduced the varieties \(\mathbb E(r, \mathfrak g)\) of r-dimensional abelian p-nilpotent subalgebras of a p-restricted Lie algebra \(\mathfrak g\) in [8]. In this paper, we identify the varieties \(\mathbb E(r, \mathfrak g)\) for a reductive restricted Lie algebra \(\mathfrak g\) and r the maximal dimension of an abelian p-nilpotent subalgebra of \(\mathfrak g\).

2000 Mathematics Subject Classification

17B50 16G10 

Notes

Acknowledgements

The first author is indebted to Eric Friedlander for generously sharing his ideas and intuition about the variety \(\mathbb E(r, \mathfrak g)\). We are also grateful to George McNinch, Paul Sobaje, and Jared Warner for sharing their expertise and patiently answering our structural questions about reductive groups in positive characteristic and to Jim Humphreys for his helpful comments. We thank the referee for a very careful reading of the paper and many helpful suggestions. We wish to acknowledge the support provided by the NSF grants DMS-0953011 and DMS-0500946.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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