DEKOMPOSISI LEVI ALJABAR LIE AFFINE FROBENIUS aff(2, R)

Authors

  • EDI KURNIADI

DOI:

https://doi.org/10.25077/jmu.10.3.229-235.2021

Abstract

Dalam artikel ini dipelajari aljabar Lie affine Frobenius aff(2, R) berdimensi 6. Aljabar Lie aff(2, R) dapat didekomposisi menggunakan dekomposisi Levi menjadi aljabar Lie linear khusus semisederhana sl(2, R) berdimensi 3, subaljabar Lie komutatif R ⊂ R2 berdimensi 2, dan split torus T berdimensi 1 sedemikian sehingga aff(2, R) = sl(2, R) ⊕ R ⊕ T. Karena aljabar Lie sl(2, R) semisederhana maka bracket Lie-nya dapat dinyatakan sebagai [sl(2, R), sl(2, R)] = sl(2, R). Selanjutnya, misalkan g = R⊕T sehingga aff(2, R) = sl(2, R) ⊕ g. Diperoleh bahwa [sl(2, R), g] ⊆ g dan [g, g] ⊆ g. Dalam hal ini, g adalah solvable radical dari aff(2, R).

Kata Kunci: Aljabar Lie affine, Aljabar Lie Semisederhana, Dekomposisi Levi

References

Ayala, V., Kizil, E., and Tribuzy, I. D. A., 2012, On an algorithm for finding

derivations of lie algebras, Proyecciones Journal of Mathematics, 31(1): 8190.

Dagli, Mehmet., 2004, Levi decomposition of Lie algebras; Algorithm for its

computation, Master of Science Thesis, Iowa State University: 1218.

Diatta, A., and Manga, B., 2014, On properties of principal elements of Frobenius Lie algebras, J. Lie Theory 24: 849 - 864.

Hendrawan, R., 2020, Aljabar Simetrik Kiri Pada Aljabar Lie Frobenius Riil

Berdimensi 6, Skripsi, tidak diterbitkan, Departemen Matematika FMIPA UNPAD

Hilgert, J., dan Neeb, K.-H., 2012, Structure and Geometry of Lie Groups, New

York: Springer Monographs in Mathematics, Springer

Humphreys, J., 1972, Introduction to Lie ALgebra and its Representation, New

York Heidelberg Berlin: Springer-Verlag

Ooms, A. I., 2009, Computing invariants and semi-invariants by means of

Frobenius Lie algebras, J. Algebra 321 : 1293 - 1312

Pham, D. N., 2016, G-Quasi-Frobenius Lie Algebras, Archivum Mathematicum,

(4): 233 - 262.

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Published

26-07-2021

Issue

Vol. 10 No. 3 (2021)

Section

Articles

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