The Leibniz-Hopf algebra is the free associative Z - algebra with one generator in each positive degree and coproduct is given by the Cartan formula. It has been also known as the ＇ring ofnoncommutative symmetric fun...The Leibniz-Hopf algebra is the free associative Z - algebra with one generator in each positive degree and coproduct is given by the Cartan formula. It has been also known as the ＇ring ofnoncommutative symmetric functions＇ [1], and to be isomorphic to the Solomon Descent algebra [ 12]. This Hopf algebra has links with algebra,topology and combinatorics. In this article we consider another approach of proof for the antipode formula in the Leibniz-Hopf algebra by using some properties of words in [2].展开更多
With the development of network economy, e-commerce platform has increasingly become a worldwide trading places of various kinds of products and services. Therefore some scholars consider, intermediaries, under the ra...With the development of network economy, e-commerce platform has increasingly become a worldwide trading places of various kinds of products and services. Therefore some scholars consider, intermediaries, under the rapid development of information technology, will gradually withdrew from the historical stage. This article carried on the thorough analysis for the reasons of the existence of electronic intermediaries, and discusses the new development space and prospect of new middlemen, from the perspective of information asymmetry of the network environment.展开更多
文摘The Leibniz-Hopf algebra is the free associative Z - algebra with one generator in each positive degree and coproduct is given by the Cartan formula. It has been also known as the ＇ring ofnoncommutative symmetric functions＇ [1], and to be isomorphic to the Solomon Descent algebra [ 12]. This Hopf algebra has links with algebra,topology and combinatorics. In this article we consider another approach of proof for the antipode formula in the Leibniz-Hopf algebra by using some properties of words in [2].
文摘With the development of network economy, e-commerce platform has increasingly become a worldwide trading places of various kinds of products and services. Therefore some scholars consider, intermediaries, under the rapid development of information technology, will gradually withdrew from the historical stage. This article carried on the thorough analysis for the reasons of the existence of electronic intermediaries, and discusses the new development space and prospect of new middlemen, from the perspective of information asymmetry of the network environment.
