Vol. 301, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Free Rota–Baxter family algebras and (tri)dendriform family algebras

Yuanyuan Zhang and Xing Gao

Vol. 301 (2019), No. 2, 741–766
DOI: 10.2140/pjm.2019.301.741
Abstract

We construct free commutative Rota–Baxter family algebras, and then free noncommutative Rota–Baxter family algebras via the method of Gröbner–Shirshov bases. We introduce the concept of dendriform (resp. tridendriform) family algebras, and prove that Rota–Baxter family algebras of weight zero (resp. λ) induce dendriform (resp. tridendriform) family algebras. We also construct free commutative dendriform (resp. tridendriform) family algebras.

Keywords
Rota–Baxter algebra, Rota–Baxter family algebra, dendriform family algebra, tridendriform family algebra, Gröbner–Shirshov basis
Mathematical Subject Classification 2010
Primary: 08B20, 13P10, 16S10, 16W99
Milestones
Received: 30 July 2018
Revised: 27 October 2018
Accepted: 29 October 2018
Published: 24 October 2019
Authors
Yuanyuan Zhang
School of Mathematics and Statistics
Lanzhou University
Lanzhou
China
Xing Gao
School of Mathematics and Statistics
Key Laboratory of Applied Mathematics and Complex Systems
Lanzhou University
Gansu
China