Double Poisson structures on finite dimensional semi-simple algebrasDouble Poisson structures on finite dimensional semi-simple algebras
Faculty of Sciences. Mathematics and Computer Science
Department of Mathematics - Computer Sciences
Algebras and representation theory. - -
11(2008):5, p. 437-460
University of Antwerp
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¡ä = 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.