CaltechAUTHORS
  A Caltech Library Service

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. https://resolver.caltech.edu/CaltechAUTHORS:20131018-083158300

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20131018-083158300

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1142/S0219498813500278 DOIArticle
http://www.worldscientific.com/doi/abs/10.1142/S0219498813500278PublisherArticle
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.
Funders:
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
NKBRPC2006CB805905
SRFDP200800550015
SRFDP20120031110022
NSFNSF-1001855
Subject Keywords:Relative Rota-Baxter operators; dendriform algebras; tridendriform algebras; Rota-Baxter operators
Other Numbering System:
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
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20131018-083158300
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41983
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Oct 2013 17:02
Last Modified:03 Oct 2019 05:54

Repository Staff Only: item control page