4 papers · 1 filter
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…
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…