by Weyer, Geert Van de

We give a description of the bimodule of double derivations 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 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.

DOI: 10.1007/s10468-008-9088-3
Online Date: 6/6/2008
Print publication date: 10/1/2008
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