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Double Poisson structures on finite dimensional semi-simple algebras

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arxiv math/0603533 v1 pith:ZP2RM6PX submitted 2006-03-22 math.AG math.RA

Geert Van de Weyer This is my paper · ORCID
classification math.AGmath.RA
keywords doublepoissonbracketsemi-simpledegreedescriptiondimensionalfinite
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We give a description of the bimodule of double derivations DDer(S) of a finite dimensional semi-simple algebra S and its double Schouten bracket in terms of a quiver. This description is used to determine which degree two monomials in T_SDDer(S) induce double Poisson brackets on S. In case S = C^n, a criterion for any degree two element to give a double Poisson bracket is deduced. For S = C^n and S' = C^m, the induced Poisson bracket on the variety of isomorphism classes of semi-simple representations iss_n(S*T) of the free product S*T is given.

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  1. Double Poisson (vertex) algebra cohomology

    math.RT 2025-09 accept novelty 8.0 of 10

    The authors define a completed double Poisson cohomology valid for all double Poisson brackets, and introduce three cohomology theories for double Poisson vertex algebras, with representation functor compatibility.

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