Title
Double Poisson structures on finite dimensional semi-simple algebrasDouble Poisson structures on finite dimensional semi-simple algebras
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Department of Mathematics - Computer Sciences
Publication type
article
Publication
Subject
Mathematics
Source (journal)
Algebras and representation theory. - -
Volume/pages
11(2008):5, p. 437-460
ISSN
1386-923X
ISI
000258896700003
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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.
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