Hokkaido Mathematical Journal

ISHIDA Tomohiko, KAWAZUMI Nariya,

The Lie algebra of rooted planar trees.

Hokkaido Mathematical Journal, 42 (2013) pp.397-416




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-Σ 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.

Uncontrolled Keywordsnonsymmetric operad, polynomial vector field