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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Contributions to the classification of simple modular Lie algebras
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by Georgia Benkart, J. Marshall Osborn and Helmut Strade
Trans. Amer. Math. Soc. 341 (1994), 227-252
DOI: https://doi.org/10.1090/S0002-9947-1994-1129435-0

Abstract:

We develop results directed towards the problem of classifying the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p > 7$. A $1$-section of such a Lie algebra relative to a torus $T$ of maximal absolute toral rank possesses a unique subalgebra maximal with respect to having a composition series with factors which are abelian or classical simple. In this paper we show that the sum $Q$ of those compositionally classical subalgebras is a subalgebra. This extends to the general case a crucial step in the classification by Block and Wilson of the restricted simple Lie algebras. We derive properties of the filtration which can be constructed using $Q$ and obtain structural information about the $1$-sections and $2$-sections of $Q$ relative to $T$. We further classify all those algebras in which $Q$ is solvable.
References
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Bibliographic Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 341 (1994), 227-252
  • MSC: Primary 17B50
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1129435-0
  • MathSciNet review: 1129435