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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Communicated by Y. Kawahigashi
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De Sole, A., Kac, V.G., Valeri, D. et al. Local and Non-local Multiplicative Poisson Vertex Algebras and Differential-Difference Equations. Commun. Math. Phys. 370, 1019–1068 (2019). https://doi.org/10.1007/s00220-019-03416-5
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DOI: https://doi.org/10.1007/s00220-019-03416-5