TY - JOUR
AU1 - Zhang, Yuanyuan
AU2 - Gao, Xing
AU3 - Manchon, Dominique
AB - In this paper, we first construct the free Rota-Baxter family algebra generated by some set X in terms of typed angularly X-decorated planar rooted trees. As an application, we obtain a new construction of the free Rota-Baxter algebra only in terms of angularly decorated planar rooted trees (not forests), which is quite different from the known construction via angularly decorated planar rooted forests by K. Ebrahimi-Fard and L. Guo. We then embed the free dendriform (resp. tridendriform) family algebra into the free Rota-Baxter family algebra of weight zero (resp. one). Finally, we prove that the free Rota-Baxter family algebra is the universal enveloping algebra of the free (tri)dendriform family algebra.
TI - Free Rota-Baxter Family Algebras and Free (tri)dendriform Family Algebras
JF - Algebras and Representation Theory
DO - 10.1007/s10468-022-10198-3
DA - 2023-12-01
UR - https://www.deepdyve.com/lp/springer-journals/free-rota-baxter-family-algebras-and-free-tri-dendriform-family-0GGMSTz2VV
SP - 2967
EP - 3002
VL - 26
IS - 6
DP - DeepDyve
ER -