Nilpotent Lie algebras in which all proper subalgebras have class at most n, II

Let be a field and let L be a finitely generated nilpotent Lie -algebra of class (exactly) c. Let n be the largest integer such that L has a proper subalgebra of class n, and let be the smallest integer such that L can be generated by d elements. In this work, we suppose that . We show that if , the...

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Bibliographic Details
Published in:Communications in algebra 2023-10, Vol.51 (10), p.4180-4184
Main Author: Evans, Martin J.
Format: Article
Language:English
Subjects:
Algebra
Integers
Lie groups
nilpotency class
Nilpotent Lie algebras
Primary: 17B05
Secondary: 17B30
Citations: Items that this one cites
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Summary:Let be a field and let L be a finitely generated nilpotent Lie -algebra of class (exactly) c. Let n be the largest integer such that L has a proper subalgebra of class n, and let be the smallest integer such that L can be generated by d elements. In this work, we suppose that . We show that if , then either and L is the unique non-abelian nilpotent Lie -algebra of dimension 3, or the characteristic of is 3, and L is a certain Lie -algebra of dimension 7 in which every maximal subalgera has class 2. We compare this with previous results that deal with the case .
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2023.2199074