# Local and Non-local Multiplicative Poisson Vertex Algebras and Differential-Difference Equations

@article{DeSole2019LocalAN,
title={Local and Non-local Multiplicative Poisson Vertex Algebras and Differential-Difference Equations},
author={Alberto De Sole and Victor G. Kac and Daniele Valeri and Minoru Wakimoto},
journal={Communications in Mathematical Physics},
year={2019},
pages={1-50}
}
• Published 5 September 2018
• Mathematics
• Communications in Mathematical Physics
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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