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Relative Rota-Baxter operators and tridendriform algebras

Bai, Chengming and Guo, Li and Ni, Xiang (2013) Relative Rota-Baxter operators and tridendriform algebras. Journal of Algebra and Its Applications, 12 (7). Art. No. 1350027. ISSN 0219-4988.

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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.

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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.
Funding AgencyGrant Number
National Natural Science Foundation of China10621101
National Natural Science Foundation of China10920161
National Natural Science Foundation of China11271202
National Natural Science Foundation of China11221091
Subject Keywords:Relative Rota-Baxter operators; dendriform algebras; tridendriform algebras; Rota-Baxter operators
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Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR3063466
Issue or Number:7
Classification Code:Mathematics Subject Classification: 17A30, 17A42, 18D50
Record Number:CaltechAUTHORS:20131018-083158300
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41983
Deposited By: Tony Diaz
Deposited On:18 Oct 2013 17:02
Last Modified:03 Oct 2019 05:54

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