Inner ideals of the special linear lie algebras of associative simple finite dimensional algebras

Shlaka, Hasan M.; Mousa, Durgham A.

doi:10.1063/5.0117506

Cited by 1 publication

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“…An inner ideal B of A (k) or K (k) is said to be Jordan-Lie if B 2 = 0. In recent paper, Shlaka and Mousa [7], studied Jordan-Lie inner ideals A (k) in the case when A is simple over an algebraically closed fields of positive characteristic. Jordan-Lie inner ideals of the Lie algebras K (k) in the case when A is simple with the symplectic involution over an algebraically closed fields of positive characteristic were also been studied by Kareem and Shlaka in [8].…”

Section: Introductionmentioning

confidence: 99%

Jordan-Lie Inner Ideals of the Orthogonal Lie Algebras

Kareem

Shlaka

2022

WJCMS

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Let be an associative algebra over a field F of any characteristic with involution * and let K=skew(A)={a in A|a*=-a} be its corresponding sub-algebra under the Lie product [a,b]=ab-ba for all a,b in A . If for some finite dimensional vector space over F and * is an adjoint involution with a symmetric non-alternating bilinear form on V , then * is said to be orthogonal. In this paper, Jordan-Lie inner ideals of the orthogonal Lie algebras were defined, considered, studied, and classified. Some examples and results were provided. It is proved that every Jordan-Lie inner ideals of the orthogonal Lie algebras is either eKe* or is a type one point space.

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Section: Introductionmentioning

confidence: 99%