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

2018/09/05 by Alberto De Sole, Victor G. Kac, Daniele Valeri +1
Mathematics · Physics and Astronomy · #math.RT #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1007/s00220-019-03416-5

42 pages

arxiv created 2018/09/05 · arxiv updated 2019/05/01

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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