Weak composition quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras
| Autor: | Guo, Li, Thibon, Jean-Yves, Yu, Houyi |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Adv Math. 344 (2019), 1-34 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aim.2018.12.001 |
| Popis: | We introduce the Hopf algebra of quasi-symmetric functions with semigroup exponents generalizing the Hopf algebra QSym of quasi-symmetric functions. As a special case we obtain the Hopf algebra WCQSym of weak composition quasi-symmetric functions, which provides a framework for the study of a question proposed by G.-C.~Rota relating symmetric type functions and Rota-Baxter algebras. We provide the transformation formulas between the weak composition monomial and fundamental quasi-symmetric functions, which extends the corresponding results for quasi-symmetric functions. Moreover, we show that QSym is a Hopf subalgebra and a Hopf quotient algebra of WCQSym. Rota's question is addressed by identifying WCQsym with the free commutative unitary Rota-Baxter algebra of weight 1 on one generator, which also allows us to equip this algebra with a Hopf algebra structure. Comment: 25 pages |
| Databáze: | arXiv |
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