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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Derivations of the Lie algebra of polynomials under Poisson bracket.


Author: L. S. Wollenberg
Journal: Proc. Amer. Math. Soc. 20 (1969), 315-320
MSC: Primary 22.90
DOI: https://doi.org/10.1090/S0002-9939-1969-0233938-1
MathSciNet review: 0233938
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Abstract: We exhibit a class of outer derivations of the Lie algebra $ P$ of complex polynomials under Poisson bracket, and prove that every derivation of $ P$ is a linear combination of one of these and an inner derivation, although this decomposition may not be unique. In particular, we show that any derivation of $ P$ which maps constants to zero must be inner. We use these results to characterise certain solutions of the Dirac problem.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1969-0233938-1
Article copyright: © Copyright 1969 American Mathematical Society