Double Multiplicative Poisson Vertex Algebras
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 onetoone 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 nonabelian integrable differentialdifference equations. A rigorous definition of double multiplicative Poisson vertex algebras in the nonlocal and rational cases is also provided.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.03418
 Bibcode:
 2021arXiv211003418F
 Keywords:

 Mathematics  Representation Theory;
 Mathematical Physics;
 Mathematics  Rings and Algebras;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 v2: 46 pages, 1 figure. Minor changes in Sections 6,7