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Free Rota–Baxter
family algebras and (tri)dendriform family algebras
Yuanyuan Zhang and Xing Gao |
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Vol. 301 (2019), No. 2, 741–766
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DOI: 10.2140/pjm.2019.301.741
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Abstract |
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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. ) induce dendriform (resp. tridendriform) family algebras. We also construct free commutative dendriform (resp. tridendriform) family algebras. |
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Keywords
Rota–Baxter algebra, Rota–Baxter family algebra, dendriform
family algebra, tridendriform family algebra,
Gröbner–Shirshov basis
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Mathematical Subject Classification 2010
Primary: 08B20, 13P10, 16S10, 16W99
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Milestones
Received: 30 July 2018
Revised: 27 October 2018
Accepted: 29 October 2018
Published: 24 October 2019
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Authors |
| Yuanyuan Zhang | |
| School of Mathematics and
Statistics Lanzhou University Lanzhou China |
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| Xing Gao | |
| School of Mathematics and
Statistics Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Gansu China |
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