The Core of Inner Ideals of Four Dimensional Real Lie Algebra With Tow Dimensional Derived
DOI:
https://doi.org/10.29304/jqcsm.2026.18.22695Keywords:
The core of E, Inner Ideal, Lie algebrasAbstract
Suppose that L is a 4-dimensional Lie algebra with a 2-dimensional derived, and E is an arbitrary non-trivial inner ideal of L. The core of E is an inner ideal of L. This paper presents a proof. If L is a 4-dimensional Lie algebra with a 2-dimensional derived algebra. Then the core of each inner ideal E of L is zero.
Downloads
References
G. Benkart , “The Lie inner ideal structure of associative rings ,” Journal of Algebra. 43 (2 ), 561 –584 (1976 ).
G. Benkart, (1977). "On inner ideals and ad-nilpotent elements of Lie algebras". Transactions of the American Mathematical Society, 232, 61-81.
G. Benkart and A. Fernández López , “The Lie inner ideal structure of associative rings revisited ,” Communications in Algebra. 37 (11 ), 3833 –3850 (2009 ).
J. Brox, A. López and M. Gómez Lozano , “Inner ideals of Lie algebras of skew elements of prime rings with involution ,” Proceedings of the American Mathematical Society. 144 (7 ), 2741 –2751 (2016 ).
A. A. Baranov, A. Mudrov, & H. M. Shlaka, (2018). "Wedderburn–Malcev decomposition of one-sided ideals of finite dimensional algebras". Communications in Algebra, 46(8), 3605-3607.
A.A. Baranov and H. Shlaka, “Jordan-Lie inner ideals of Finite dimensional associative algebras”, Journal of Pure and Applied Algebra, vol. 224, no. 5, pp. 106189, 2020.
Hamood, J. S., & Shlaka, H. M. "The Core of Inner ideal of Real Four-Dimensional Lie Algebra with One Dimensional Derived".
A. F. López , E. García and M. G. Lozano , “An Artinian theory for Lie algebras ,” Journal of Algebra. 319 (3 ), 938 –951 (2008 ).
A. F. López , E. García , M. G. , Lozano and E. Neher , “A construction of gradings of Lie algebras ,” International Mathematics Research Notices. 2007 (9 ), rnm051 –rnm051 (2007 ).
A. A. E. Premet , “Lie algebras without strong degeneration ,” Mathematics of the USSR-Sbornik. 57 (1 ), 151 (1987 ).
Saeed, H. S. (2022), "Classification of Inner ideals of Two, Three and Four Dimensional Lie Algebras" MSc Thesis University of Kufa.
Schöbel, C. (1993), "A Classification of Real Finite-dimensional Lie Algebras With a Low-Dimensional Derived Algebra". Reports on Mathematical Physics, 33(1-2),175-186.
H. M. Shlaka, and F. S. Kareem, “Abelian Non Jordan-Lie Inner Ideals of the Orthogonal Finite Dimensional Lie Algebras”, Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, no. 5, pp. 1547-1561, 2022.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Firdous Kareem Mohammed, Hasan Mohammed Ali
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
