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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 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Duality theories for metabelian Lie algebras
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by Michael A. Gauger PDF
Trans. Amer. Math. Soc. 187 (1974), 89-102 Request permission

Abstract:

This paper is concerned with duality theories for metabelian (2-step nilpotent) Lie algebras. A duality theory associates to each metabelian Lie algebra N with cod ${N^2} = g$, another such algebra ${N_D}$ satisfying ${({N_D})_D} \cong N,{N_1} \cong {N_2}$ if and only if ${({N_1})_D} \cong {({N_2})_D}$, and if $\dim N = g + p$ then $\dim {N_D} = g + (_2^g) - p$. The obvious benefit of such a theory lies in its reduction of the classification problem.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 187 (1974), 89-102
  • MSC: Primary 17B30
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0342576-8
  • MathSciNet review: 0342576