Some results on isoclinism in Lie algebras

Subject Areas : Statistics

Homayoon Arabiani ¹ (Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran)
Hamid Darabi ² (Department of Mathematics, Esfarayen University of Technology, Esfarayen, Iran.)

Received: 2019-12-16 Accepted : 2020-09-23 Published : 2021-03-01

Keywords: زیرجبر فراتینی, n-آیزوکلینیسم, جبر لی تنه‌ای,

Abstract :

T h e iso clinism o f L i e algebra i s widely used i n the classification o f Lie algebra. This concept has a weaker structure than t h e concept o f the isomorphism. T h e iso clinism o f Lie algebra was first introduced by the Moneyhun and later it is generalized by others to n- iso clinism in Lie algebra, as well as, to the iso clinism in a pair of Lie algebra in the literature. In this paper, we study the n- isoclinism in Lie algebra and prove some of the features of the n- iso clinism in Lie algebra. For example, we prove that if L 1 and L 2 are two Lie algebras that the intersection of their centroid and F rattini algebra are zero, then, the iso clinism L 1 and L 2 are equivalent to their central factors.

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