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## THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS

#### Donald Yau [1]

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Motivated by recent work on Hom-Lie algebras and the HomYang-Baxter equation, we introduce a twisted generalization of the classical Yang-Baxter equation (CYBE), called the classical Hom-Yang-Baxter equation (CHYBE). We show how an arbitrary solution of the CYBE induces multiple infinite families of solutions of the CHYBE. We also introduce the closely related structure of Hom-Lie bialgebras, which generalize Drinfel’d’s Lie bialgebras. In particular, we study the questions of duality and cobracket perturbation and the sub-classes of coboundary and quasi-triangular Hom-Lie bialgebras.
The classical Hom-Yang-Baxter equation, Hom-Lie bialgebra
Konular JA98RG24KE Makaleler Yazar: Donald Yau
 Bibtex @ { ieja266210, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2015}, volume = {17}, pages = {11 - 45}, doi = {10.24330/ieja.266210}, title = {THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS}, key = {cite}, author = {Yau, Donald} } APA Yau, D . (2015). THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS. International Electronic Journal of Algebra, 17 (17), 11-45. DOI: 10.24330/ieja.266210 MLA Yau, D . "THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS". International Electronic Journal of Algebra 17 (2015): 11-45 Chicago Yau, D . "THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS". International Electronic Journal of Algebra 17 (2015): 11-45 RIS TY - JOUR T1 - THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS AU - Donald Yau Y1 - 2015 PY - 2015 N1 - doi: 10.24330/ieja.266210 DO - 10.24330/ieja.266210 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 11 EP - 45 VL - 17 IS - 17 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266210 UR - http://dx.doi.org/10.24330/ieja.266210 Y2 - 2018 ER - EndNote %0 International Electronic Journal of Algebra THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS %A Donald Yau %T THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS %D 2015 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 17 %N 17 %R doi: 10.24330/ieja.266210 %U 10.24330/ieja.266210 ISNAD Yau, Donald . "THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS". International Electronic Journal of Algebra 17 / 17 (Haziran 2015): 11-45. http://dx.doi.org/10.24330/ieja.266210