Double multiplicative Poisson vertex algebras
We develop the theory of double multiplicative Poisson vertex algebras. These structures, defined at the level of associative algebras, are shown to be such that they induce a classical structure of multiplicative Poisson vertex algebra on the corresponding representation spaces. Moreover, we prove that they are in one-to-one correspondence with local lattice double Poisson algebras, a new important class among Van den Bergh’s double Poisson algebras. We derive several classification results, and we exhibit their relation to non-abelian integrable differential-difference equations. A rigorous definition of double multiplicative Poisson vertex algebras in the non-local and rational cases is also provided.
University of Glasgow
Project MMNLP (Mathematical Methods in Non Linear Physics) of the INFN
- Mathematical Sciences
Published inInternational Mathematics Research Notices
PublisherOxford University Press
- AM (Accepted Manuscript)
Rights holder© The Authors
Publisher statementThis is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Maxime Fairon, Daniele Valeri, Double Multiplicative Poisson Vertex Algebras, International Mathematics Research Notices, 2022;, rnac245, https://doi.org/10.1093/imrn/rnac245 is available online at: https://doi.org/10.1093/imrn/rnac245.