## ISHIDA Tomohiko, KAWAZUMI Nariya,

## The Lie algebra of rooted planar trees.

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

### Fulltext

PDF### 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-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.

MSC(Primary) | 18D50 |
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MSC(Secondary) | 57R32 |

Uncontrolled Keywords | nonsymmetric operad, polynomial vector field |