The Lie algebra of rooted planar trees

Abstract

We study a natural Lie algebra structure on the free vector space generated by all rooted planar trees as the associated Lie algebra of the nonsymmetric operad (non-$\Sigma$ operad, preoperad) of rooted planar trees. We determine whether the Lie algebra and some related Lie algebras are finitely generated or not, and prove that a natural surjection called the augmentation homomorphism onto the Lie algebra of polynomial vector fields on the line has no splitting preserving the units.

arXiv comment14 pages

References in corpus (2)

• An application of the second Riemann continuation theorem to cohomology of the Lie algebra of vector fields on the complex line
• The center of the Goldman Lie algebra of a surface of infinite genus