The Core of Inner ideal of Real Four Dimensional Lie Algebra With One Dimensional Derived

jaafar sadiq

doi:10.31185/wjps.387

Authors

jaafar sadiq university of kufa

DOI:

https://doi.org/10.31185/wjps.387

Keywords:

Lie algebras, The core_L(V), Sandwich element

Abstract

Suppose that V is any inner ideal of L. The core of V is an inner ideal of L with special requirement. In this paper we prove. If L is a 4-dimension Lie algebra a with 1-dimensional derived , then the core of every inner ideal of L is zero. Moreover L containing a sandwich elements if L' not subset of Z and every element in L is sandwich if L' subset of Z.

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References

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

G. Benkart and A. Fernández López , “The Lie inner ideal structure of associative rings revisited ,” Communica-tions 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. Premet , “Inner ideals in modular Lie algebras ,” Vestsī Akad. Navuk BSSR Ser. Fīz.-Mat. Navuk , 5 , 11 –15 (1986 ).

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

A. F. López , E. García and M. G. Lozano , “An Artinian theory for Lie algebras ,” Journal of Algebra. 319 (3 ), 938 –951 (2008 ).

H. M. Shlaka, and D. A. Mousa, (2023) “Inner ideals of the special linear Lie algebras of associative simple finite dimensional algebras”, AIP Conference Proceedings AIP Publishing LLC, 2414(1), 040070.

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

H. M. Shlaka , “Generalization of Jordan-Lie of Finite Dimensional Associative Algebras ,” arXiv preprint arXiv:2107.00775 (2021 ).

A. F. López , E. García , M. G. , Lozano and E. Neher , “A construction of gradings of Lie algebras ,” Interna-tional Mathematics Research Notices. 2007 (9 ), rnm051 –rnm051 (2007 ).

Shlaka, H. S., & Saeed, H. S. (2023, December). Inner ideals of the two and three-dimensional lie algebras. In AIP Conference Proceedings (Vol. 2834, No. 1). AIP Publishing.‏

K. Erdmann and M. J. Wildon , “Introduction to Lie algebras ,” Springer Science & Business Media 1-23 (2006 ).

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.

Cohen, A.M.(2021).Inner ideals in Lie algebras and sphericalbuild- ings. Indagationes Mathemati-cae,32(5),1115-1138.

Schöbel, C. (1993). A classification of real finite dimensional Lie algebras with alow-dimensional derived al-gebra .Reports on Math- ematical Physics,33(1-2),175-186.