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O-operators on associative algebras and associative Yang–Baxter equations

Bai, Chengming and Guo, Li and Ni, Xiang (2012) O-operators on associative algebras and associative Yang–Baxter equations. Pacific Journal of Mathematics, 256 (2). pp. 257-289. ISSN 0030-8730.

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An O-operator on an associative algebra is a generalization of a Rota–Baxter operator that plays an important role in the Hopf algebra approach of Connes and Kreimer to the renormalization of quantum field theory. It is also the associative analog of an O-operator on a Lie algebra in the study of the classical Yang–Baxter equation. We introduce the concept of an extended O-operator on an associative algebra whose Lie algebra analog has been applied to generalized Lax pairs and PostLie algebras. We study algebraic structures coming from extended O-operators. Continuing the work of Aguiar deriving Rota–Baxter operators from the associative Yang–Baxter equation, we show that its solutions correspond to extended O-operators through a duality. We also establish a relationship of extended O-operators with the generalized associative Yang–Baxter equation.

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Additional Information:© 2012 by Pacific Journal of Mathematics. Received April 14, 2011. Revised August 5, 2011; Accepted 27 September 2011; Published 30 May 2012. C. Bai is supported by NSFC grants 10621101 and 10920161, NKBRPC grant 2006CB805905 and SRFDP grant 200800550015. L. Guo is supported by NSF grant DMS 0505445 and DMS-1001855 and thanks the Chern Institute of Mathematics at Nankai University for hospitality. Li Guo is the corresponding author.
Funding AgencyGrant Number
NSFC (China)10621101
NSFC (China)10920161
Subject Keywords:O-operator, Rota–Baxter operator, Yang–Baxter equation, bimodule
Issue or Number:2
Classification Code:MSC2010: primary 16W99, 17A30; secondary 57R56.
Record Number:CaltechAUTHORS:20120723-123234827
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32648
Deposited By: Aucoeur Ngo
Deposited On:23 Jul 2012 20:28
Last Modified:03 Oct 2019 04:02

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