8 papers
Modules and operator rings of Reynolds algebras
Jun He, Xiao-Song Peng, Chenghao Zhang +1
We develop a module theory for weighted Reynolds algebras by constructing an associa?tive ring that records the algebra action and the module operator. The categories of left and r…
Monoidal structure on Rota-Baxter algebras via augmentation, and free cocycle bialgebras
Li Guo, Yunzhou Xie, Yi Zhang
A tensor product is known for commutative Rota--Baxter algebras through a universal construction, but its underlying algebra need not be the ordinary tensor product an…
Rota-Baxter operators and factorization of Lie affgebras
JiaJia Han, Abror Khudoyberdiyev, Yunzhou Xie +1
We introduce Rota-Baxter operators on Lie affgebras by an identity independent of the choice of origin and prove that they induce descendant Lie affgebra structures. We establish a…
Generalized Connes-Kreimer Hopf algebras on decorated rooted forests by weighted cocycles
Fei Wang, Li Guo, Yi Zhang
The Connes-Kreimer Hopf algebra of rooted trees is an operated Hopf algebra whose coproduct satisfies the classical Hochschild 1-cocycle condition. In this paper, we extend the set…
Cocycle weighted infinitesimal bialgebras and pre-Lie algebras on rooted trees
Loïc Foissy, Yunzhou Xie, Dawei Zhang +1
The concept of weighted infinitesimal bialgebras provides an algebraic framework for understanding the non-homogeneous associative Yang-Baxter equation. In this paper, we endow the…
Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach
Loic Foissy, Xiao-Song Peng, Yunzhou Xie +1
In this paper, we first endow the space of decorated planar rooted forests with a coproduct that equips it with the structure of a bialgebra and further a Moerdijk Hopf algebra. We…
Multiple Rota-Baxter algebra and multiple Rota-Baxter modules
Jun He, Xiaosong Peng, Yi Zhang
In this paper, we develop the theory of multiple Rota-Baxter modules over multiple Rota-Baxter algebras. We introduce left, right, and bimodule structures and construct free -op…
The Cohomology of relative cocycle weighted Reynolds operators and NS-pre-Lie algebras
Guo Shuangjian, Zhang Yi
Unifying various generalizations of the important notions of Reynolds operators, the relative cocycle weighted Reynolds operators are studied. Here cocycle weighted means the weigh…