On the Hopf Algebra of Rooted Trees

Details On the Hopf Algebra of Rooted Trees On the Hopf Algebra of Rooted Trees

2007-10-30

arxiv.org/abs/0710.5646v2

Physics

Mathematical Physics

7pages

Scientific paper

We find a formula to compute the number of the generators, which generate the $n$-filtered space of Hopf algebra of rooted trees, i.e. the number of equivalent classes of rooted trees with weight $n$. Applying Hopf algebra of rooted trees, we show that the analogue of Andruskiewitsch and Schneider's Conjecture is not true. The Hopf algebra of rooted trees and the enveloping algebra of the Lie algebra of rooted trees are two important examples of Hopf algebras. We give their representation and show that they have not any nonzero integrals. We structure their graded Drinfeld doubles and show that they are local quasitriangular Hopf algebras.

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