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Title
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Double Poisson structures on finite dimensional semi-simple algebras
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Author
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Abstract
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| 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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Language
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English
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Source (journal)
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Algebras and representation theory. - -
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Publication
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2008
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ISSN
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1386-923X
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DOI
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10.1007/S10468-008-9088-3
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Volume/pages
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11
:5
(2008)
, p. 437-460
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ISI
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000258896700003
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Full text (Publisher's DOI)
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