A Complex Higher-Dimensional Lie Algebra with Real and Imaginary Structure Constants as Well as Its Decomposition |
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Authors: | ZHANG Yu-Feng |
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Affiliation: | Mathematical School, Liaoning Normal University, Dalian 116029, China |
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Abstract: | A new Lie algebra G of the Lie algebra sl(2) is constructedwith complex entries whose structure constants are real andimaginary numbers. A loop algebra ˜G corresponding to the Lie algebra G is constructed, for which it is devoted togenerating a soliton hierarchy of evolution equations under theframework of generalized zero curvature equation which is derivedfrom the compatibility of the isospectral problems expressed byHirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra ˜G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain itsbi-Hamiltonian structure by employing the quadratic-form identity. |
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Keywords: | complex Lie algebra structure constant loop algebra bi-Hamiltonian structure |
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