Hokkaido Mathematical Journal

The Lie algebra of rooted planar trees

Tomohiko ISHIDA and Nariya KAWAZUMI

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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.

Article information

Source
Hokkaido Math. J., Volume 42, Number 3 (2013), 397-416.

Dates
First available in Project Euclid: 12 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1384273389

Digital Object Identifier
doi:10.14492/hokmj/1384273389

Mathematical Reviews number (MathSciNet)
MR3137392

Zentralblatt MATH identifier
1284.18020

Subjects
Primary: 18D50: Operads [See also 55P48]
Secondary: 57R32: Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]

Keywords
nonsymmetric operad polynomial vector field

Citation

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


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