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 |
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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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