• Corpus ID: 202558455

L-infinity bialgebroids and homotopy Poisson structures on supermanifolds

  title={L-infinity bialgebroids and homotopy Poisson structures on supermanifolds},
  author={Theodore Th. Voronov},
  journal={arXiv: Differential Geometry},
  • T. Voronov
  • Published 11 September 2019
  • Mathematics
  • arXiv: Differential Geometry
We generalize to the homotopy case a result of K. Mackenzie and P. Xu on relation between Lie bialgebroids and Poisson geometry. For a homotopy Poisson structure on a supermanifold $M$, we show that $(TM, T^*M)$ has a canonical structure of an $L_{\infty}$-bialgebroid. (Higher Koszul brackets on forms introduced earlier by H. Khudaverdian and the author are part of one of its manifestations.) The underlying general construction is that of a "(quasi)triangular" $L_{\infty}$-bialgebroid, which is… 
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