2007/10/30 by Weicai Wu, Wu, Weicai, Yao-Zhong Zhang +5
Mathematics · #16W30 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.0710.5646
openalex publication_date 2007/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.