In this study, we give necessary and sufficient conditions on the equalities of the central automorphisms group of 𝐿𝑚,𝑘 to the IAautomorphisms group and inner automorphisms group of 𝐿𝑚,𝑘.
📌 3 Key Takeaways
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Objective & Hypothesis:Let 𝐿𝑚,𝑘 be the free nilpotent Lie algebra of class 𝑘 that of finite rank 𝑚, 𝑚 ≥ 2 over a field of characteristic zero.
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Key Findings & Data:Let 𝐿𝑚,𝑘 be the free nilpotent Lie algebra of class 𝑘 that of finite rank 𝑚, 𝑚 ≥ 2 over a field of characteristic zero.
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Conclusion & Impact:In this study, we give necessary and sufficient conditions on the equalities of the central automorphisms group of 𝐿𝑚,𝑘 to the IAautomorphisms group and inner automorphisms group of 𝐿𝑚,𝑘.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let 𝐿𝑚,𝑘 be the free nilpotent Lie algebra of class 𝑘 that of finite rank 𝑚, 𝑚 ≥ 2 over a field of characteristic zero. In this study, we give necessary and sufficient conditions on the equalities of the central automorphisms group of 𝐿𝑚,𝑘 to the IAautomorphisms group and inner automorphisms group of 𝐿𝑚,𝑘.
Özet
𝐿𝑚,𝑘 karakteristiği sıfır olan bir cisim üzerinde sonlu 𝑚, 𝑚 ≥ 2 rankına sahip, 𝑘 −yıncı sınıftan serbest nilpotent Lie cebiri olsun. 𝐿𝑚,𝑘 nın merkezi otomorfizmler grubunun bu cebirin 𝐼𝐴 −otomorfizmler grubu ile iç otomorfizmler grubuna eşit olması için gerek ve yeter koşulları belirledik.
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Cite This Article
ÖZTEKİN, Ö., ESKAL, C. (2019). On The Automorphism Groups of Free Nilpotent Lie Algebras. ACADEMIC PLATFORM-JOURNAL OF ENGINEERING AND SCIENCE, Cilt: 7 - Sayı: 3, 403–405. https://ajindex.com/articles/354902
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