Some Notes on the Dual Leibniz-Hopf algebra  

作　　者：Neset Deniz Turgay 

出　　处：《Journal of Mathematics and System Science》2013年第11期573-576,共4页数学和系统科学（英文版）

摘　　要：The Leibniz-Hopf algebra is the free associative algebra with one generator in each positive degree and coproduct given by the Cartan formula. Quasi-symmetric functions are a generalisation of symmetric functions [7],and the algebra of quasi-symmetric functions appear as the dual of the Leibniz-Hopf algebra. The Leibniz-Hopf algebra and its dual are word Hopf algebras and play an important role in combinatorics, algebra and topology. We give some properties of words and consider an another view of proof for the antipode in the dual Leibniz-Hopf algebra.

关 键 词：Hopf algebra Leibniz-Hopf algebra ANTIPODE quasi-symmetric functions. 

分 类 号：O153.3[理学—数学] O172[理学—基础数学]