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- W4224442677 abstract "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 $operatorname{Rep}(A,n)$ 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 $Aotimes A$. 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 formalisation of the widespread tensor notation used to write Poisson brackets of matrices in mathematical physics." @default.
- W4224442677 created "2022-04-27" @default.
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- W4224442677 date "2022-04-07" @default.
- W4224442677 modified "2023-09-29" @default.
- W4224442677 title "Around Van den Bergh's double brackets for different bimodule structures" @default.
- W4224442677 doi "https://doi.org/10.48550/arxiv.2204.03298" @default.
- W4224442677 hasPublicationYear "2022" @default.
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