Levi Decomposition of Frobenius Lie Algebra of Dimension 6

Henti Henti, Edi Kurniadi, Ema Carnia

Abstract


In this paper, we study notion of the Lie algebra  of dimension 6. The finite dimensional Lie algebra can be expressed in terms of decomposition between Levi subalgebra and the maximal solvable ideal. This form of decomposition is called Levi decomposition. The work aims to obtain Levi decomposition of Frobenius Lie algebra of dimension 6. To achieve this aim, we compute Levi subalgebra and the maximal solvable ideal (radical) of  with respect to its basis. To obtain Levi subalgebra and the maximal solvable ideal, we apply literature reviews about Lie algebra and decomposition Levi in Dagli result. For future research, decomposition Levi for higher dimension of Frobenius Lie algebra  is still an open problem.

Keywords


Frobenius Lie algebra; Levi Decomposition; Lie algebra; radical.

Full Text:

PDF

References


J. E. Humphreys, Introduction to Lie Algebras and Representation Theory. Springer, 1972.

M. A. Alvarez, M. C. Rodríguez-Vallarte, and G. Salgado, “Contact and Frobenius solvable Lie algebras with abelian nilradical,” Commun. Algebr., vol. 46, no. 10, pp. 4344–4354, 2018, doi: 10.1080/00927872.2018.1439048.

P. Turkowski, “Low-dimensional real Lie algebras,” J. Math. Phys., vol. 29, no. 10, pp. 2139–2144, 1988, doi: 10.1063/1.528140.

M. Rais, “La représentation coadjointe du groupe affine,” vol. 4, pp. 913–937, 1978.

A. Diatta and B. Manga, “On properties of principal elements of frobenius lie algebras,” J. Lie Theory, vol. 24, no. 3, pp. 849–864, 2018.

B. Csikós and L. Verhóczki, “Classification of frobenius Lie algebras of dimension ≤ 6,” Publ. Math., vol. 70, no. 3–4, pp. 427–451, 2007.

E. Kurniadi, E. Carnia, and A. K. Supriatna, “The construction of real Frobenius Lie algebras from non-commutative nilpotent Lie algebras of dimension,” J. Phys. Conf. Ser., vol. 1722, no. 1, 2021, doi: 10.1088/1742-6596/1722/1/012025.

Henti, E. Kurniadi, and E. Carnia, “On Frobenius functionals of the Lie algebra M3(ℝ) ⊕ gl3(ℝ),” J. Phys. Conf. Ser., vol. 1872, no. 1, 2021, doi: 10.1088/1742-6596/1872/1/012015.

Henti, E. Kurniadi, and E. Carnia, “Quasi Associative ALgebras on the Frobenius Lie Algebra M3(ℝ) ⊕ gl3(ℝ),” Al-Jabar J. Pendidik. Mat., vol. 12, no. 1, pp. 1–16, 2021, [Online]. Available: http://ejournal.radenintan.ac.id/index.php/al-jabar/article/view/2014/1564.

E. Kurniadi and H. Ishi, “Harmonic analysis for 4-dimensional real frobenius lie algebras,” Springer Proc. Math. Stat., vol. 290, no. March, pp. 95–109, 2019, doi: 10.1007/978-3-030-26562-5_4.

M. Dagli, “Levi Decomposition of Lie Algebras; Algorithms for its Computation,” Iowa State University, 2004.

J. Hilgert and K.-H. Neeb, Structure and Geometry of Lie Groups. New York: Springer Monographs in Mathematics, 2012.

A. I. Ooms, On frobenius lie algebras, vol. 8, no. 1. 1980.




DOI: https://doi.org/10.18860/ca.v7i3.15656

Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Henti Henti, Edi Kurniadi, Ema Carnia

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.