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Double multiplicative Poisson vertex algebras

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posted on 2022-08-25, 09:26 authored by Maxime Fairon, Daniele Valeri

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.

Funding

University of Glasgow

Project MMNLP (Mathematical Methods in Non Linear Physics) of the INFN

History

School

  • Science

Department

  • Mathematical Sciences

Published in

International Mathematics Research Notices

Volume

2023

Issue

17

Pages

14991–15072

Publisher

Oxford University Press

Version

  • AM (Accepted Manuscript)

Rights holder

© The Authors

Publisher statement

This 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.

Acceptance date

2022-08-18

Publication date

2022-09-13

Copyright date

2022

ISSN

1073-7928

eISSN

1687-0247

Language

  • en

Depositor

Dr Maxime Fairon. Deposit date: 24 August 2022

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