Inner Ideals of the Real Five-Dimensional Lie Algebras with Two-Dimensional Derived, Such That l′ ⊈ z

mustafa shamkhi

doi:10.31185/wjps.365

Authors

mustafa shamkhi University of Kufa, Faculty of Computer Science and Mathematics, Department of Mathematics

DOI:

https://doi.org/10.31185/wjps.365

Abstract

Abstract— Inner ideal of the five-dimensional non-commutative Lie alge- bras over the real fields with two-dimensional derived were classified. It is proved that one, two, three and four-dimensional inner ideals are exist in every five-dimensional Lie algebra. It is also proved that five-dimensional Lie algebras contain inner ideals which are neither ideals nor sub-algebras

References

A. A. Baranov, A. Mudrov, and H. M. Shlaka (2018) Wedderburn-Malcev decompo- sition of one-sided ideals of finite dimensional algebras, Communications in Algebra 46(8), 3605-3607.

A. Baranov, and H. M. Shlaka, (2020) Jordan-Lie inner ideals of finite dimensional associative algebras. Journal of Pure and Applied Algebra, 224(5), 106189.

G. Benkart (1976) The Lie inner ideal structure of associative rings, Journal of Algebra, 43(2), 561-584.

G. Benkart (1977) On inner ideals and ad-nilpotent elements of Lie algebras, Trans- actions of the American Mathematical Society, 232, 61-81.

G. Benkart, and A. Fern´andez L´opez (2009) The Lie inner ideal structure of asso- ciative rings revisited, Communications in Algebra, 37(11), 3833-3850.

J. Brox, A. Fern´andez L´opez, and M. G´omez Lozano (2016) Inner ideals of Lie alge- bras of skew elements of prime rings with involution, Proceedings of the American Mathematical Society, 144(7), 2741-2751.

K. Erdmann, and M. J. Wildon (2006) Introduction to Lie algebras, Springer Science & Business Media, London Vol(122).

A Fern´andez L´opez, E. Garc´ıa, and M. G´omez Lozano (2008) An Artinian theory for Lie algebras. Journal of Algebra, 319(3), 938-951.

A. Fern´andez L´opez, E. Garc´ıa, M. G´omez Lozano, and E. Neher (2007) A con- struction of gradings of Lie algebras, International Mathematics Research Notices, 9, rnm051-rnm051.

F. S. Kareem, and H. M. Shlaka, 2022 Inner Ideals of the Symplectic Simple Lie Algebra, Journal of Physics: Conference Series, IOP Publishing 2322(1), 012058.

A. A. Premet (1987) Lie algebras without strong degeneration, Mathematics of the USSR-Sbornik, 57(1), 151.

H. S. Saeed and H. M . Shlaka (2023) Inner ideals of Four-Dimensional Real Lie Algebras with One-Dimensional Derivation, Journal of Physics: Conference Series, IOP Publishing, (to appear).

C. Sch¨obel (1993) A Classification of the Real Finite-Dimensional Lie Algebras with a Low-Dimensional Derived Algebra. Reports on Mathematical Physics, 33(1- 2), 175-186.

H. M. Shlaka (2023) Generalization of Jordan-Lie of Finite Dimensional Associative Algebras, Journal of Algebra and Its Applications 22(12): 2350266.

H. M. Shlaka, and F. S. Kareem (2022) Abelian Non Jordan-Lie Inner Ideals of the Orthogonal Finite Dimensional Lie Algebras, Journal of Discrete Mathematical Sciences and Cryptography, 25(5), 1547-1561.

H. M. Shlaka, and D. A. Mousa (2023) Inner Ideals of The Special Linear Lie Algebras of Associative Simple Finite Dimensional Algebras, AIP Conference Pro- ceedings, AIP Publishing LLC, 2414(1), 040070.

H. Shlaka, and H. S. Saeed (2023) Inner Ideals of The Two and Three-Dimensional Lie Algebras, AIP Conference Proceedings, AIP Publishing LLC 2834(1), 080052.