Cyclic pairings and derived Poisson structures

2018/10/10 by Ramadoss, Ajay C., Zhang, Yining
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1810.04798

Abstract

There is a canonical derived Poisson structure on the universal enveloping algebra U\mathfraka of a (DG) Lie algebra \mathfraka that is Koszul dual to a cyclic cocommutative (DG) coalgebra. Interesting special cases of this derived Poisson structure include (an analog of) the Chas-Sullivan bracket on string topology. We study how certain derived character of \mathfraka intertwine this derived Poisson structure with the induced Poisson structure on the representation homology of \mathfraka. In addition, we obtain an analog of one of our main results for associative algebras.

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• Noncommutative Poisson structures, derived representation schemes and Calabi-Yau algebras
• Dual Hodge decompositions and derived Poisson brackets
• The derived non-commutative Poisson bracket on Koszul Calabi-Yau algebras
• Shifted double Poisson structures and noncommutative Poisson extensions
• Algebraic string bracket as a Poisson bracket