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- Title
Three Ideals of Lie Superalgebras.
- Authors
Zhao, Xiaodong; Chen, Liangyun
- Abstract
We define perfect ideals, near perfect ideals and upper bounded ideals of a finite-dimensional Lie superalgebra, and study the properties of these three kinds of ideals through their relevant sequences. We prove that a Lie superalgebra is solvable if and only if its maximal perfect ideal is zero, or its quotient superalgebra by the maximal perfect ideal is solvable. We also show that a Lie superalgebra is nilpotent if and only if its maximal near perfect ideal is zero. Moreover, we prove that a nilpotent Lie superalgebra has only one upper bounded ideal, which is the nilpotent Lie superalgebra itself.
- Subjects
LIE superalgebras
- Publication
Algebra Colloquium, 2022, Vol 29, Issue 1, p143
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386722000116