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Transactions of the American Mathematical Society

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

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Left-symmetric algebras for $\mathfrak {gl}(n)$
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by Oliver Baues PDF
Trans. Amer. Math. Soc. 351 (1999), 2979-2996 Request permission

Abstract:

We study the classification problem for left-symmetric algebras with commutation Lie algebra ${\mathfrak {gl}}(n)$ in characteristic $0$. The problem is equivalent to the classification of étale affine representations of ${\mathfrak {gl}}(n)$. Algebraic invariant theory is used to characterize those modules for the algebraic group $\operatorname {SL}(n)$ which belong to affine étale representations of ${\mathfrak {gl}}(n)$. From the classification of these modules we obtain the solution of the classification problem for ${\mathfrak {gl}}(n)$. As another application of our approach, we exhibit left-symmetric algebra structures on certain reductive Lie algebras with a one-dimensional center and a non-simple semisimple ideal.
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Additional Information
  • Oliver Baues
  • Affiliation: Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitäts- strasse 1, D-40225 Düsseldorf, Germany
  • Address at time of publication: Department of Mathematics, ETH-Zentrum, CH-8092 Zürich, Switzerland
  • Email: oliver@math.ethz.ch
  • Received by editor(s): February 10, 1997
  • Published electronically: March 8, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 2979-2996
  • MSC (1991): Primary 55N35, 55Q70, 55S20
  • DOI: https://doi.org/10.1090/S0002-9947-99-02315-6
  • MathSciNet review: 1608273