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A constructive method for decomposing real representations. (English) Zbl 07312483
Summary: A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the computer algebra system GAP4.
MSC:
17B45 Lie algebras of linear algebraic groups
20C40 Computational methods (representations of groups) (MSC2010)
16Z05 Computational aspects of associative rings (general theory)
17B81 Applications of Lie (super)algebras to physics, etc.
Software:
CoReLG; GAP
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References:
[1] Ali, S.; Azad, H.; Biswas, I.; Ghanam, R.; Mustafa, M. T., Embedding algorithms and applications to differential equations, J. Symb. Comput., 86, 166-188 (2018) · Zbl 1432.17002
[2] Azad, H.; Biswas, I.; Ghanam, R.; Mustafa, M. T., On computing joint invariants of vector fields, J. Geom. Phys., 97, 69-76 (2015) · Zbl 1376.37050
[3] Čap, A.; Slovák, J., Parabolic Geometries. I. Background and General Theory, Mathematical Surveys and Monographs, vol. 154 (2009), American Mathematical Society: American Mathematical Society Providence, RI · Zbl 1183.53002
[4] Dietrich, H.; Faccin, P.; de Graaf, W. A., CoReLG, computation with real Lie groups, Version 1.53 (2019), Refereed GAP package
[5] The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.10.2 (2019)
[6] Goto, M.; Grosshans, F. D., Semisimple Lie Algebras, Lecture Notes in Pure and Applied Mathematics, vol. 38 (1978), Marcel Dekker, Inc.: Marcel Dekker, Inc. New York-Basel · Zbl 0391.17004
[7] de Graaf, W. A., Lie Algebras: Theory and Algorithms, North-Holland Mathematical Library, vol. 56 (2000), Elsevier Science: Elsevier Science Amsterdam · Zbl 1122.17300
[8] de Graaf, W. A., Computation with Linear Algebraic Groups, Monographs and Research Notes in Mathematics (2017), CRC Press: CRC Press Boca Raton, FL · Zbl 06690823
[9] de Graaf, W. A.; Marrani, A., Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8, J. Phys. A, 53, Article 155203 pp. (2020)
[10] Hilgert, J.; Neeb, K.-H., Structure and Geometry of Lie Groups (2011), Springer-Verlag: Springer-Verlag New York
[11] Knapp, A. W., Lie Groups Beyond an Introduction, Progress in Mathematics, vol. 140 (2002), Birkhäuser Boston, Inc.: Birkhäuser Boston, Inc. Boston, MA · Zbl 1075.22501
[12] Onishchik, A. L., Lectures on Real Semisimple Lie Algebras and Their Representations, ESI Lectures in Mathematics and Physics (2004), European Mathematical Society: European Mathematical Society Zürich · Zbl 1080.17001
[13] Steinberg, R., Lectures on Chevalley groups (1968), Yale University: Yale University New haven, CT, Notes prepared by J. Faulkner and R. Wilson
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