Events Calendar
Oct 2
14:00 - 15:00
Mathematical Physics & Integrable Systems seminar: Jing Ping Wang (University of Kent)
SMSAS Mathematical Physics seminars
Hamiltonian and preHamiltonian and Nijenhuis operators

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.


Sibson Building (SibSR2)
United Kingdom


Open to All interested persons,

Contact: Dr Pavlos Xenitidis
School of Mathematics, Statistics and Actuarial Science


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Last Updated: 10/01/2012