Abstract
We will show that, on the space C ∞ (X) of smooth functions on a symplectic manifold, there are some canonical n-ary operations generalizing the multiplication of functions and the Poisson bracket. For various n, these canonical operations generate an operad which is not of finite type. In particular some of these operations cannot be expressed in terms of Poisson brackets and multiplications. These operations are closely related to harmonic polynomials (in a generalized sense).
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This paper is respectfully dedicated to I. M. Gelfand
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© 1995 Birkhäuser Boston
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Mathieu, O. (1995). The Symplectic Operad. In: Gindikin, S., Lepowsky, J., Wilson, R.L. (eds) Functional Analysis on the Eve of the 21st Century. Progress in Mathematics, vol 131/132. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2582-9_8
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DOI: https://doi.org/10.1007/978-1-4612-2582-9_8
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