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arXiv · 1810.04798

Cyclic pairings and derived Poisson structures

Ajay C. Ramadoss·Yining Zhang
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Abstract

There is a canonical derived Poisson structure on the universal enveloping algebra $\mathcal{U}\mathfrak{a}$ of a (DG) Lie algebra $\mathfrak{a}$ 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 $\mathfrak{a}$ intertwine this derived Poisson structure with the induced Poisson structure on the representation homology of $\mathfrak{a}$. In addition, we obtain an analog of one of our main results for associative algebras.

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Ajay C. Ramadoss, Yining Zhang. 2018-10-10. Cyclic pairings and derived Poisson structures. https://arxiv.org/abs/1810.04798

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