On Behavior of Solvable Ideals of Lie Algebras Under Outer Derivations |
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Authors: | Anatoliy P Petravchuk |
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Institution: | 1. Department of Algebra and Mathematical Logic, Faculty of Mechanics and Mathematics , Kyiv Taras Shevchenko University , Kyiv, Ukraine aptr@univ.kiev.ua |
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Abstract: | Let L be a finite dimensional Lie algebra over a field F. It is well known that the solvable radical S(L) of the algebra L is a characteristic ideal of L if char F = 0, and there are counterexamples to this statement in case char F = p > 0. We prove that the sum S(L) of all solvable ideals of a Lie algebra L (not necessarily finite dimensional) is a characteristic ideal of L in the following cases: 1) char F = 0; 2) S(L) is solvable and its derived length is less than log2 p. |
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Keywords: | Characteristic ideal Derivation Derivated length Lie algebra |
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