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Ngày xuất bản:
20/05/2025
Số lượt xem tóm tắt: 11
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Số lượt xem PDF: 3
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Trích dẫn bài báo
Ta, T. Q., & Nguyen, T. M. T. (2025). A computer algebra approach for verifying isomorphism of Lie algebras. Tạp chí Khoa học Đại học Đồng Tháp, 14(02S), 12-21. https://doi.org/10.52714/dthu.14.02S.2025.1635
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A computer algebra approach for verifying isomorphism of Lie algebras
Nội dung chính của bài viết
Tóm tắt
This paper proposes a computer algebra method for verifying the isomorphism of finite-dimensional Lie algebras over the complex field. Afterwards, an example is analyzed to demonstrate the suggested method. Finally, its efficiency is shown through applications.
Từ khóa
Isomorphism verifying, Lie algebras, Maple
Chi tiết bài viết
Bài báo này được cấp phép theo Creative Commons Attribution-NonCommercial 4.0 International License.
Tài liệu tham khảo
Chen, C. (2011). Solving polynomial systems via triangular decomposition. PhD dissertation. Ontario, Canada: Western University. Retrieved from https://ir.lib.uwo.ca/etd/255
Chen, C., & Maza, M. M. (2012). Algorithms for computing triangular decomposition of polynomial systems. J. Symbolic Comput., 47(6), 610-642. https://doi.org/10.1016/j.jsc.2011.12.023
Cox, D. A., Little, J., & O’shea, D. (2015). Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (4th ed.). Switzerland: Springer Cham. https://doi.org/10.1007/978-3-319-16721-3
Gerdt, V. P., & Lassner, W. (1993). Isomorphism verification for complex and real Lie algebras by Groebner basis technique. In N. H. Ibragimov, M. Torrisi, & A. Valenti (Ed.), Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics (pp. 245-254). Dordrecht: Springer. https://doi.org/10.1007/978-94-011-2050-0_25
Gong, M. P. (1998). Classification of nilpotent Lie algebras of dimension 7 (Over algebraically closed fields and R). PhD dissertation. Ontario, Canada: University of Waterloo. Retrieved from https://hdl.handle.net/10012/1148
Hindeleh, F., & Thompson, G. (2008). Seven dimensional Lie algebras with a four dimensional nilradical. Algebras Groups Geom, 25(3), 243-265.
Le, A. V., Nguyen, A. T., Nguyen, T. C. T., Nguyen, T. M. T., & Vo, N. T. . (2023). Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals. . Comm. Algebra, 51(5), 1866-1885. https://doi.org/10.1080/00927872.2022.2145300
Lemaire, F., Maza, M. M., Pana, W., Xie, Y. (2011). When does ⟨T ⟩ equal sat(T )? J. Symbolic Comput., J. Symbolic Comput., 1291-1305. https://doi.org/10.1016/j.jsc.2011.08.010
Mubarakzyanov, G. M. (1966). Some Theorems on Solvable Lie Algebras. Izv Vyssh Uchebn Zaved Mat., 55(6), 95-98.
Parry, A. R. (2007). A classification of real indecomposable solvable Lie algebras of small dimension with codimension one nilradicals. Master thesis. Utah, USA.: Utah State University. Retrieved from https://digitalcommons.usu.edu/etd/7145
Snobl, L., & Winternitz, P. (2014). Classification and Identification of Lie Algebras. CRM Monograph Series (Volume 33). Rhode Island, USA: American Mathematical Society. https://doi.org/10.1090/crmm/033
Turkowski, P. (1990). Solvable Lie algebras of dimension six. J. Math. Phys., 31(6), 1344–1350. https://doi.org/10.1063/1.528721
Chen, C., & Maza, M. M. (2012). Algorithms for computing triangular decomposition of polynomial systems. J. Symbolic Comput., 47(6), 610-642. https://doi.org/10.1016/j.jsc.2011.12.023
Cox, D. A., Little, J., & O’shea, D. (2015). Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (4th ed.). Switzerland: Springer Cham. https://doi.org/10.1007/978-3-319-16721-3
Gerdt, V. P., & Lassner, W. (1993). Isomorphism verification for complex and real Lie algebras by Groebner basis technique. In N. H. Ibragimov, M. Torrisi, & A. Valenti (Ed.), Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics (pp. 245-254). Dordrecht: Springer. https://doi.org/10.1007/978-94-011-2050-0_25
Gong, M. P. (1998). Classification of nilpotent Lie algebras of dimension 7 (Over algebraically closed fields and R). PhD dissertation. Ontario, Canada: University of Waterloo. Retrieved from https://hdl.handle.net/10012/1148
Hindeleh, F., & Thompson, G. (2008). Seven dimensional Lie algebras with a four dimensional nilradical. Algebras Groups Geom, 25(3), 243-265.
Le, A. V., Nguyen, A. T., Nguyen, T. C. T., Nguyen, T. M. T., & Vo, N. T. . (2023). Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals. . Comm. Algebra, 51(5), 1866-1885. https://doi.org/10.1080/00927872.2022.2145300
Lemaire, F., Maza, M. M., Pana, W., Xie, Y. (2011). When does ⟨T ⟩ equal sat(T )? J. Symbolic Comput., J. Symbolic Comput., 1291-1305. https://doi.org/10.1016/j.jsc.2011.08.010
Mubarakzyanov, G. M. (1966). Some Theorems on Solvable Lie Algebras. Izv Vyssh Uchebn Zaved Mat., 55(6), 95-98.
Parry, A. R. (2007). A classification of real indecomposable solvable Lie algebras of small dimension with codimension one nilradicals. Master thesis. Utah, USA.: Utah State University. Retrieved from https://digitalcommons.usu.edu/etd/7145
Snobl, L., & Winternitz, P. (2014). Classification and Identification of Lie Algebras. CRM Monograph Series (Volume 33). Rhode Island, USA: American Mathematical Society. https://doi.org/10.1090/crmm/033
Turkowski, P. (1990). Solvable Lie algebras of dimension six. J. Math. Phys., 31(6), 1344–1350. https://doi.org/10.1063/1.528721