Free Rota-Baxter Family Algebras and Free (tri)dendriform Family Algebras
| Autor: | Yuanyuan Zhang, Xing Gao, Dominique Manchon |
|---|---|
| Přispěvatelé: | Department of Mathematics and Statistics [Lanzhou], Lanzhou University, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Manchon, Dominique |
| Rok vydání: | 2023 |
| Předmět: |
Rings and Algebras (math.RA)
Mathematics::Quantum Algebra General Mathematics Mathematics::Rings and Algebras [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA] FOS: Mathematics [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA] Mathematics - Rings and Algebras 16W99 16S10 13P10 08B20 |
| Zdroj: | Algebras and Representation Theory. |
| ISSN: | 1572-9079 1386-923X |
| DOI: | 10.1007/s10468-022-10198-3 |
| Popis: | 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. Reference precised in the introduction. This text uses in an essential way the description of the free dendriform and tridendriform family algebras given in arXiv:1909.08946 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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