M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra

Details M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra

2010-09-08

arxiv.org/abs/1009.1654v2

Mathematics

Quantum Algebra

23 Figures

Scientific paper

We show that the zeroth cohomology of Kontsevich's graph complex is isomorphic to the Grothendieck-Teichm\"uller Lie algebra grt. The map is explicitly described. This result has applications to deformation quantization and Duflo theory. Also, it allows proving the freeness part of the Deligne-Drinfeld conjecture in some low orders. As a side result one obtains that the homotopy deformations of the Gerstenhaber operad are parameterized by grt. Finally, our methods give a second proof of a result of H. Furusho, stating that the pentagon equation for grt-elements implies the hexagon equation.

Affiliated with

Also associated with

No associations

Rating

M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-558011