Results Math 72 (2017), 145–170
2016 Springer International Publishing
published online December 30, 2016
Results in Mathematics
Some Results on Rota–Baxter
Tianshui Ma and Huihui Zheng
Abstract. We give constructions of Rota–Baxter monoidal Hom-
(co)algebras from Hom-Hopf module (co)algebras, and then introduce
the concept of Rota–Baxter monoidal Hom-bialgebras. Furthermore, we
consider the relations between Rota–Baxter monoidal Hom-systems and
monoidal Hom-dendriform algebras, and also derive the structures of pre-
Lie Hom-(co)algebras via Rota–Baxter monoidal Hom-(co)algebras of dif-
Mathematics Subject Classiﬁcation. 16T05, 17B05, 16W99.
Keywords. Rota–Baxter monoidal Hom-(co)algebra, Rota–Baxter monoidal
Hom-system, monoidal Hom-dendriform algebra, Radford biproduct,
Rota–Baxter monoidal Hom-bialgebra.
Rota–Baxter algebras were introduced in [18,19] in the context of diﬀerential
operators on commutative Banach algebras and since  intensively studied
in probability and combinatorics, and more recently in mathematical physics,
such as dendriform algebras (see ), free Rota–Baxter algebras (see [6,7]), etc.
One can refer to the book  for the detailed theory of Rota–Baxter algebras.
In 2014, Jian in  constructed Hopf module algebras via Yetter-Drinfeld
module algebras and derived the corresponding Rota–Baxter algebras. Based
on the dual method in the Hopf algebra theory, Jian and Zhang in intro-
duced the notion of Rota–Baxter coalgebras and also provided various exam-
ples of the new object, including constructions by group-like elements and by
smash coproduct. In 2015, Ma and Liu gave the deﬁnition of Rota–Baxter bial-
gebras by combining Rota–Baxter algebras and coalgebras, and also provided
examples from Radford biproduct Hopf algebras (see ).