Double Multiplicative Poisson Vertex Algebras

Maxime Fairon; Daniele Valeri

doi:10.1093/imrn/rnac245

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arXiv · 2110.03418

Double Multiplicative Poisson Vertex Algebras

Maxime Fairon·Daniele Valeri

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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.

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BibTeX RIS

Maxime Fairon, Daniele Valeri. 2021-10-07. Double Multiplicative Poisson Vertex Algebras. https://doi.org/10.1093/imrn%2Frnac245

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