Around Van den Bergh s double brackets for different bimodule structures.pdf (2.85 MB)
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Around Van den Bergh’s double brackets for different bimodule structures

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journal contribution
posted on 2023-01-20, 11:34 authored by Maxime Fairon, Colin McCulloch
A double Poisson bracket, in the sense of M. Van den Bergh, is an operation on an associative algebra A which induces a Poisson bracket on each representation space Rep(A,n) in an explicit way. In this note, we study the impact of changing the Leibniz rules underlying a double bracket. This change amounts to make a suitable choice of A-bimodule structure on A⊗A. In the most important cases, we describe how the choice of A-bimodule structure fixes an analogue to Jacobi identity, and we obtain induced Poisson brackets on representation spaces. The present theory also encodes a formalization of the widespread tensor notation used to write Poisson brackets of matrices in mathematical physics

Funding

University of Glasgow

Loughborough University

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Communications in Algebra

Publisher

Taylor & Francis

Version

VoR (Version of Record)

Rights holder

©The Author(s)

Publisher statement

This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Acceptance date

2022-10-16

Publication date

2022-11-09

Copyright date

2022

ISSN

0092-7872

eISSN

1532-4125

Language

en

Depositor

Dr Maxime Fairon. Deposit date: 19 January 2023