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arXiv · 1809.01735

Local and non-local multiplicative Poisson vertex algebras and differential-difference equations

Alberto De Sole·Victor G. Kac·Daniele Valeri·Minoru Wakimoto
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Abstract

We develop the notions of multiplicative Lie conformal and Poisson vertex algebras, local and non-local, and their connections to the theory of integrable differential-difference Hamiltonian equations. We establish relations of these notions to $q$-deformed $W$-algebras and lattice Poisson algebras. We introduce the notion of Adler type pseudodifference operators and apply them to integrability of differential-difference Hamiltonian equations.

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Alberto De Sole, Victor G. Kac, Daniele Valeri, Minoru Wakimoto. 2018-09-05. Local and non-local multiplicative Poisson vertex algebras and differential-difference equations. https://doi.org/10.1007/s00220-019-03416-5

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