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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 823756, 11 pages
http://dx.doi.org/10.1155/2015/823756
Research Article

Hom--Operators and Hom-Yang-Baxter Equations

College of Science, Nanjing Agricultural University, Nanjing 210095, China

Received 3 May 2015; Accepted 21 July 2015

Academic Editor: Juan C. Marrero

Copyright © 2015 Yuanyuan Chen and Liangyun Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In Hom-Lie set, we introduce the concept of Hom--operators and study its relation with classical Hom-Yang-Baxter equation, as well as left-symmetric Hom-algebras. We construct the corresponding relation between left-symmetric Hom-algebras and Hom-1-cocycles, which are both related to classical Hom-Yang-Baxter equation. Moreover, in Hom-algebra setting, we establish the equivalent relationship between AHYBE (associative Hom-Yang-Baxter equations) and -operators on Frobenius monoidal Hom-algebras.