Relative Rota-Baxter operators and tridendriform algebras
- Creators
- Bai, Chengming
- Guo, Li
- Ni, Xiang
Abstract
A relative Rota–Baxter operator is a relative generalization of a Rota–Baxter operator on an associative algebra. In the Lie algebra context, it is called an O-operator, originated from the operator form of the classical Yang–Baxter equation. We generalize the well-known construction of dendriform and tridendriform algebras from Rota–Baxter algebras to a construction from relative Rota–Baxter operators. In fact we give two such generalizations, on the domain and range of the operator respectively. We show that each of these generalized constructions recovers all dendriform and tridendriform algebras. Furthermore the construction on the range induces bijections between certain equivalence classes of invertible relative Rota–Baxter operators and tridendriform algebras.
Additional Information
© 2013 World Scientific Publishing Company. Received 27 May 2012; Accepted 21 December 2012; Published 15 May 2013. Communicated by L. Bokut. C. Bai thanks the support by the National Natural Science Foundation of China (10621101, 10920161, 11271202 and 11221091), NKBRPC (2006CB805905) and SRFDP (200800550015 and 20120031110022). L. Guo thanks the NSF grant DMS-1001855 for support, and thanks the Chern Institute of Mathematics at Nankai University for their hospitality. The authors thank the referee for valuable suggestions.Additional details
- Eprint ID
- 41983
- DOI
- 10.1142/S0219498813500278
- Resolver ID
- CaltechAUTHORS:20131018-083158300
- 10621101
- National Natural Science Foundation of China
- 10920161
- National Natural Science Foundation of China
- 11271202
- National Natural Science Foundation of China
- 11221091
- National Natural Science Foundation of China
- 2006CB805905
- NKBRPC
- 200800550015
- SRFDP
- 20120031110022
- SRFDP
- NSF-1001855
- NSF
- Created
-
2013-10-18Created from EPrint's datestamp field
- Updated
-
2021-11-10Created from EPrint's last_modified field
- Other Numbering System Name
- MathSciNet Review
- Other Numbering System Identifier
- MR3063466