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- Title
Double Multiplicative Poisson Vertex Algebras.
- Authors
Fairon, Maxime; Valeri, Daniele
- Abstract
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.
- Subjects
POISSON algebras; ASSOCIATIVE algebras; DIFFERENTIAL-difference equations; REPRESENTATIONS of algebras
- Publication
IMRN: International Mathematics Research Notices, 2023, Vol 2023, Issue 17, p14991
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnac245