6 papers · 1 filter
Extending structures of Rota-Baxter Lie algebras
Xiao-song Peng, Yi Zhang
In this paper, we first introduce the notion of an extending datum of a Rota-Baxter Lie algebra through a vector space. We then construct a unified product for the Rota-Baxter Lie…
Commutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebras
Xing Gao, Li Guo, Yi Zhang
The Rota-Baxter algebra and the shuffle product are both algebraic structures arising from integral operators and integral equations. Free commutative Rota-Baxter algebras provide…
Matching Hom-Setting of Rota-Baxter algebras, dendriform algebras and pre-Lie algebras
Dan Chen, Xiao-Song Peng, Chia Zargeh +1
In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras and matching (pre)Lie algebras. Moreover, we…
Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras
Xing Gao, Li Guo, Yi Zhang
We introduce the notion of a matching Rota-Baxter algebra motivated by the recent work on multiple pre-Lie algebras arising from the study of algebraic renormalization of regularit…
Hopf algebras of planar binary trees: an operated algebra approach
Yi Zhang, Xing Gao
Parallel to operated algebras built on top of planar rooted trees via the grafting operator , we introduce and study -algebras and more generally -algebras based…
Weighted infinitesimal unitary bialgebras on rooted forests and weighted cocycles
Yi Zhang, Dan Chen, Xing Gao +1
In this paper, we define a new coproduct on the space of decorated planar rooted forests to equip it with a weighted infinitesimal unitary bialgebraic structure. We introduce the c…