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

Alberto De Sole; Victor G. Kac; Daniele Valeri; Minoru Wakimoto

doi:10.1007/s00220-019-03416-5

paper

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

arXiv:1809.01735 · doi:10.1007/s00220-019-03416-5

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.

42 pages