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}
}
• Published 2009
• Mathematics
• Letters in Mathematical Physics
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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