The applications of a higher-dimensional Lie algebra and its decomposed subalgebras |
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| Authors: | Zhang Yu Yufeng Zhang |
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| Institution: | 1. Division of Medical Oncology, Sunnybrook Odette Cancer Centre, Toronto, Canada;2. Imaging Research, Sunnybrook Research Institute, Toronto and Dept Medical Biophysics, University of Toronto, Canada;3. Department of Medical Imaging, Sunnybrook Health Sciences Centre, Toronto, Canada;4. Joint Department of Medical Imaging, University of Toronto Health Network, Toronto, Canada;5. Department of Research Design and Biostatistics, Sunnybrook Health Sciences Centre, Toronto, Canada;1. Laboratory of Systems Biology and Bioinformatics (LBB), Institute of Biochemistry and Biophysics, University of Tehran, Tehran, Iran;2. National Research Council Canada, Montreal, QC H4P 2R2, Canada;3. Center for Bioinformatics, McGill University, Montreal, QC H3G 0B1, Canada;1. Institute of the History of Medicine, Giessen University, D-35392 Giessen, Germany;2. Boston Children''s Hospital, Harvard Medical School, Boston, MA, USA;3. Medical Education Center, Faculty of Medicine, The Hebrew University of Jerusalem, Jerusalem, Israel;1. Department of General Surgery, The Second Xiang-ya Hospital, Central South University, Changsha 410011, China;2. Department of Gastroduodenal and Pancreatic surgery, Translation Medicine Research Center of Liver, Cancer Hospital and Affiliated Cancer Hospital of Xiangya College, Central South University, Changsha 410013, China;3. College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China;1. Department of Biophysics, Biology Faculty, M.V. Lomonosov Moscow State University, 119992 Moscow, Russia;2. Technical University Berlin, Institute of Chemistry, Max-Volmer-Laboratory of Biophysical Chemistry, Straβe des 17. Juni 135, D-10623 Berlin, Germany |
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| Abstract: | With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 × 6 matrix Lie algebra sμ(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra sμ(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras sμ(6) and E is used to directly construct integrable couplings. |
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