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UID:33922
DTSTAMP:20191016T002009Z
SUMMARY:Mathematical Physics & Integrable Systems seminar: Jing Ping Wang (University of Kent)
LOCATION:SR2, Sibson Building (SibSR2)
DESCRIPTION:We introduce preHamiltonian pairs of difference operators and study their connections with Nijenhuis and Hamiltonian operators. A difference operator is called preHamiltonian if its image is a Lie subalgebra with respect to the Lie bracket of evolutionary vector fields on a difference field. Two preHamiltonian operators form a preHamiltonian pair if any their linear combination is preHamiltonian. Then we show that preHamiltonian pairs naturally lead to Nijenhuis operators. Moreover, Nijenhuis operators can be represented in terms of a preHamiltonian pair. This provides a systematic method to check whether a rational operator is Nijenhuis. We explore the link between preHamiltonian and Hamiltonian operators and show that if H is a rational Hamiltonian operator, then to find a second Hamiltonian operator K compatible with H is the same as to find a preHamiltonian pair A and B such that K=A B-1 H is skew-symmetric. In the end, we illustrate our theory on known and new examples. This is the joint work with S. Carpentier and A.V. Mikhailov.\n\n
DTSTART:20181002T130000Z
DTEND:20181002T140000Z
URL:
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