Lie symmetries of the Chow group of a Jacobian and the tautological subring

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Let $J$ be the Jacobian of a smooth projective curve. We define a natural action of the Lie algebra of polynomial Hamiltonian vector fields on the plane, vanishing at the origin, on the Chow group of $J$ with rational coefficients. Using this action we obtain some relations between tautological cycles on $J$.
AMSLatex, 15 pages

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