The 6=3×2 huge Lie algebra Ξ of all local and non-local differential operators on a circle is applied to the standard Adler-Kostant-Symes (AKS) R-bracket scheme. It is shown in particular that there exist three additional Lie structures, associated to three graded modified classical Yang-Baxter (GMCYB) equations. As we know from the standard case, these structures can be used to classify in a more consistent way a wide class of integrable systems. Other algebraic properties are also presented.
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International Journal of Sustainable and Green Energy (Volume 4, Issue 3-2)
This article belongs to the Special Issue Wind-Generated Waves, 2D Integrable KdV Hierarchies and Solitons |
| DOI | 10.11648/j.ijrse.s.2015040302.13 |
| Page(s) | 10-16 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Huge Lie Algebra, Graded Modified Classical Yang-Baxter Equations, Integrable Hamiltonian Systems
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APA Style
Mahmoud Akdi, Amina Boulahoual, Moulay Brahim Sedra. (2014). Note on the 3-Graded Modified Classical Yang-Baxter Equations and Integrable Systems. International Journal of Sustainable and Green Energy, 4(3-2), 10-16. https://doi.org/10.11648/j.ijrse.s.2015040302.13
ACS Style
Mahmoud Akdi; Amina Boulahoual; Moulay Brahim Sedra. Note on the 3-Graded Modified Classical Yang-Baxter Equations and Integrable Systems. Int. J. Sustain. Green Energy 2014, 4(3-2), 10-16. doi: 10.11648/j.ijrse.s.2015040302.13
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Download@article{10.11648/j.ijrse.s.2015040302.13,
author = {Mahmoud Akdi and Amina Boulahoual and Moulay Brahim Sedra},
title = {Note on the 3-Graded Modified Classical Yang-Baxter Equations and Integrable Systems},
journal = {International Journal of Sustainable and Green Energy},
volume = {4},
number = {3-2},
pages = {10-16},
doi = {10.11648/j.ijrse.s.2015040302.13},
url = {https://doi.org/10.11648/j.ijrse.s.2015040302.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijrse.s.2015040302.13},
abstract = {The 6=3×2 huge Lie algebra Ξ of all local and non-local differential operators on a circle is applied to the standard Adler-Kostant-Symes (AKS) R-bracket scheme. It is shown in particular that there exist three additional Lie structures, associated to three graded modified classical Yang-Baxter (GMCYB) equations. As we know from the standard case, these structures can be used to classify in a more consistent way a wide class of integrable systems. Other algebraic properties are also presented.},
year = {2014}
}
TY - JOUR T1 - Note on the 3-Graded Modified Classical Yang-Baxter Equations and Integrable Systems AU - Mahmoud Akdi AU - Amina Boulahoual AU - Moulay Brahim Sedra Y1 - 2014/11/11 PY - 2014 N1 - https://doi.org/10.11648/j.ijrse.s.2015040302.13 DO - 10.11648/j.ijrse.s.2015040302.13 T2 - International Journal of Sustainable and Green Energy JF - International Journal of Sustainable and Green Energy JO - International Journal of Sustainable and Green Energy SP - 10 EP - 16 PB - Science Publishing Group SN - 2575-1549 UR - https://doi.org/10.11648/j.ijrse.s.2015040302.13 AB - The 6=3×2 huge Lie algebra Ξ of all local and non-local differential operators on a circle is applied to the standard Adler-Kostant-Symes (AKS) R-bracket scheme. It is shown in particular that there exist three additional Lie structures, associated to three graded modified classical Yang-Baxter (GMCYB) equations. As we know from the standard case, these structures can be used to classify in a more consistent way a wide class of integrable systems. Other algebraic properties are also presented. VL - 4 IS - 3-2 ER -
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