Hokkaido Mathematical Journal
- Hokkaido Math. J.
- Volume 42, Number 3 (2013), 397-416.
The Lie algebra of rooted planar trees
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.
Hokkaido Math. J., Volume 42, Number 3 (2013), 397-416.
First available in Project Euclid: 12 November 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 18D50: Operads [See also 55P48]
Secondary: 57R32: Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]
ISHIDA, Tomohiko; KAWAZUMI, Nariya. The Lie algebra of rooted planar trees. Hokkaido Math. J. 42 (2013), no. 3, 397--416. doi:10.14492/hokmj/1384273389. https://projecteuclid.org/euclid.hokmj/1384273389