论文标题
免费的rota-baxter家族代数和免费（TRI）树突状家庭代数
Free Rota-Baxter family algebras and Free (tri)dendriform family algebras
论文作者
论文摘要
在本文中，我们首先构建了由某些$ x $产生的自由rota-baxter家族代数，就键入的$ x $装修的平面生根树而言。作为一种应用，我们仅根据装饰有角的平面树（不是森林）来获得免费的rota-baxter代数的新结构，这与K. ebrahimi-fard和L. guo通过K. eb. ebrahimi-fard和L. guo的已知结构完全不同。然后，我们将自由树突形（tridendriform）家族代数嵌入重量零的自由rota-baxter家族代数（一个分别）。最后，我们证明了自由rota-baxter家族代数是自由（TRI）齿状族家族代数的通用代数。
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.
