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Transactions of the American Mathematical Society

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

 

 

Duality theories for metabelian Lie algebras


Author: Michael A. Gauger
Journal: Trans. Amer. Math. Soc. 187 (1974), 89-102
MSC: Primary 17B30
MathSciNet review: 0342576
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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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DOI: https://doi.org/10.1090/S0002-9947-1974-0342576-8
Article copyright: © Copyright 1974 American Mathematical Society