Double multiplicative Poisson vertex algebras

Fairon, M. and Valeri, D. (2023) Double multiplicative Poisson vertex algebras. International Mathematics Research Notices, 2023(17), pp. 14991-15072. (doi: 10.1093/imrn/rnac245)

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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.

Item Type:Articles
Additional Information:M.F. is supported by a Rankin-Sneddon Research Fellowship of the University of Glasgow. D.V. acknowledges the financial support of the project MMNLP (Mathematical Methods in Non Linear Physics) of the INFN.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Fairon, Dr Maxime and Valeri, Dr Daniele
Authors: Fairon, M., and Valeri, D.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:International Mathematics Research Notices
Publisher:Oxford University Press
ISSN:1073-7928
ISSN (Online):1687-0247
Published Online:13 September 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in International Mathematics Research Notices 2023(17):14991-15072
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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