The Principal Element of a Frobenius Lie Algebra

@article{Gerstenhaber2009ThePE,
  title={The Principal Element of a Frobenius Lie Algebra},
  author={Murray Gerstenhaber and Anthony Giaquinto},
  journal={Letters in Mathematical Physics},
  year={2009},
  volume={88},
  pages={333-341}
}
We introduce the notion of the principal element of a Frobenius Lie algebra $${\frak{f}}$$ . The principal element corresponds to a choice of $${F \in \frak{f}^{*}}$$ such that F[–, –] non-degenerate. In many natural instances, the principal element is shown to be semisimple, and when associated to sln, its eigenvalues are integers and are independent of F. For certain “small” functionals F, a simple construction is given which readily yields the principal element. When applied to the first… Expand
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© Annales de l’institut Fourier, 1978, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditionsExpand
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