Weak c-ideals of Leibniz algebras

A subalgebra B of a Leibniz algebra L is called a weak c-ideal of L if there is a subideal C of L such that and where is the largest ideal of L contained in B. This is analogous to the concept of a weakly c-normal subgroup, which has been studied by a number of authors. We obtain some properties of...

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Bibliographic Details
Published in:Communications in algebra 2023-11, Vol.51 (11), p.4676-4685
Main Authors: Towers, David A., Ciloglu, Zekiye
Format: Article
Language:English
Subjects:
Algebra
Frattini ideal
Leibniz algebra
Lie groups
Solvable
Subgroups
Supersolvable
Symmetric Leibniz algebra
Weak c-ideal
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Summary:A subalgebra B of a Leibniz algebra L is called a weak c-ideal of L if there is a subideal C of L such that and where is the largest ideal of L contained in B. This is analogous to the concept of a weakly c-normal subgroup, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterizations of solvable and supersolvable Leibniz algebras generalizing previous results for Lie algebras. We note that one-dimensional weak c-ideals are c-ideals, and show that a result of Turner classifying Leibniz algebras in which every one-dimensional subalgebra is a c-ideal is false for general Leibniz algebras, but holds for symmetric ones.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2023.2215340