8 papers
Fertility fibres and coproduct coefficients in the LOT Hopf algebra
Zhicheng Zhu, Jingtao Li, Xing Gao
We study fibres of the fertility map from decorated rooted trees to decorated multi-index monomials. For a multi-index of weight , the fibre $\mathcal F_{\math…
Banach fixed point and flow approach for rough analysis
Yvain Bruned, Yingtong Hou, Paul Laubie +1
In this paper, we show that the main algebraic assumption required to perform a fixed point argument for rough differential equations implies the algebraic assumption for the Baill…
Controlled rough paths: a general Hopf-algebraic setting
Zhicheng Zhu, Xing Gao, Nannan Li +1
We set up controlled rough paths for a class of combinatorial Hopf algebras, encompassing shuffle, Butcher-Connes-Kreimer and Munthe-Kaas--Wright Hopf algebras. The class of contro…
Free Novikov algebras and the Hopf algebra of decorated multi-indices
Zhicheng Zhu, Xing Gao, Dominique Manchon
We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multi-indices that recently appeared in the literature, which can be briefly described as the gr…
A Poincaré-Birkhoff-Witt theorem for the universal enveloping algebra of a Rota-Baxter Lie algebra
Zhi-Cheng Zhu, Xing Gao, Li Guo +1
Rota-Baxter associative algebras and Rota-Baxter Lie algebras are both important in mathematics and mathematical physics, with the former a basic structure in quantum field renorma…
Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects
Xing Gao, Li Guo, Yanjun Liu +1
Groups with various types of operators, in particular the recently introduced Rota-Baxter groups, have generated renowned interest with close connections to numerical integrals, Ya…