A note on noncommutative Poisson structures

2005/06/14 by William Crawley-Boevey, Crawley-Boevey, William
Mathematics · #16W25 #17B63 #53D30 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16W25 #msc:17B63 #msc:53D30

paper · pdf · doi:10.48550/arxiv.math/0506268

6 pages

arxiv created 2005/06/14 · arxiv updated 2009/12/01

Abstract

We introduce a new type of noncommutative Poisson structure on associative algebras. It induces Poisson structures on the moduli spaces classifying semisimple modules. Path algebras of doubled quivers and preprojective algebras have noncommutative Poisson structures given by the necklace Lie algebra.

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