Traveling is one major theme of Fitzgerald's novel Tender Is the Night. This fashionable activity for the 1920 s Americans is represented in the novel as ostensibly bearing different meanings to the main character...Traveling is one major theme of Fitzgerald's novel Tender Is the Night. This fashionable activity for the 1920 s Americans is represented in the novel as ostensibly bearing different meanings to the main characters, but a deeper look would reveal that it is unanimously resorted to as a weapon against the spiritual barrenness caused by the cult of business, and more importantly, as a way to the experience of rootedness.展开更多
In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests mo...In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].展开更多
文摘Traveling is one major theme of Fitzgerald's novel Tender Is the Night. This fashionable activity for the 1920 s Americans is represented in the novel as ostensibly bearing different meanings to the main characters, but a deeper look would reveal that it is unanimously resorted to as a weapon against the spiritual barrenness caused by the cult of business, and more importantly, as a way to the experience of rootedness.
基金Supported by NSFC(No.12101316)Belt and Road Innovative Talents Exchange Foreign Experts project(No.DL2023014002L)。
文摘In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].
