Derivations of the Lie algebra of polynomials under Poisson bracket.
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- by L. S. Wollenberg PDF
- Proc. Amer. Math. Soc. 20 (1969), 315-320 Request permission
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
- Herbert Goldstein, Classical Mechanics, Addison-Wesley Press, Inc., Cambridge, Mass., 1951. MR 0043608
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793 G. W. Mackey, Mathematical foundations of quantum mechanics, Benjamin, New York, 1963, Chapter 1. L. S. Wollenberg, Ph.D. thesis, Oxford, 1967.
- J.-M. Souriau, Quantification géométrique, Comm. Math. Phys. 1 (1966), 374–398 (French, with English summary). MR 207332
- R. F. Streater, Canonical quantization, Comm. Math. Phys. 2 (1966), 354–374. MR 220490
- Léon Van Hove, Sur certaines représentations unitaires d’un groupe infini de transformations, Acad. Roy. Belg. Cl. Sci. Mém. Coll. in 8$^\circ$ 26 (1951), no. 6, 102 (French). MR 57260
Additional Information
- © Copyright 1969 American Mathematical Society
- 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