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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 16th 2010
   • (edited Sep 16th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexWhen I told him about it today, Dmitry Roytenberg urged that we highlight a bit more visibly a fact that was mentioned on the nLab before, but not highlighted maybe sufficiently. Namely by the general theory of [[infinity-Lie algebra cohomology]] we have for every $\infty$-Lie algebroid $\mathfrak{a}$ equipped with an [[invariant polynomial]] $\omega$ the corresponding Chern-Simons $CS_\omega \in W(\mathfrak{a})$ wich exhibits the transgression to the corresponding $\infty$-Lie algebroid cocycle. If you apply this general theory to a [[Poisson Lie algebroid]], then then Chern-Simons form that drops out is the action functional of the [[Poisson sigma-model]]. I added this remark more visibly now to [[Poisson Lie algebroid]], [[Poisson sigma-model]] and [[infinity-Lie algebroid cohomology]].

   When I told him about it today, Dmitry Roytenberg urged that we highlight a bit more visibly a fact that was mentioned on the nLab before, but not highlighted maybe sufficiently.

   Namely by the general theory of infinity-Lie algebra cohomology we have for every $\infty$-Lie algebroid $\mathfrak{a}$ equipped with an invariant polynomial $\omega$ the corresponding Chern-Simons $CS_\omega \in W(\mathfrak{a})$ wich exhibits the transgression to the corresponding $\infty$-Lie algebroid cocycle.

   If you apply this general theory to a Poisson Lie algebroid, then then Chern-Simons form that drops out is the action functional of the Poisson sigma-model.

   I added this remark more visibly now to Poisson Lie algebroid, Poisson sigma-model and infinity-Lie algebroid cohomology.