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February 2013 The Lie algebra of rooted planar trees
Tomohiko ISHIDA, Nariya KAWAZUMI
Hokkaido Math. J. 42(3): 397-416 (February 2013). DOI: 10.14492/hokmj/1384273389

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.

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Tomohiko ISHIDA. Nariya KAWAZUMI. "The Lie algebra of rooted planar trees." Hokkaido Math. J. 42 (3) 397 - 416, February 2013. https://doi.org/10.14492/hokmj/1384273389

Information

Published: February 2013
First available in Project Euclid: 12 November 2013

zbMATH: 1284.18020
MathSciNet: MR3137392
Digital Object Identifier: 10.14492/hokmj/1384273389

Subjects:
Primary: 18D50
Secondary: 57R32

Rights: Copyright © 2013 Hokkaido University, Department of Mathematics

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Vol.42 • No. 3 • February 2013
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