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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We further show that there is also a one-to-one correspondence between generalized orthogonal derivations (resp. generalized orthogonal automorphisms) on generalized metric $n$-Leibniz algebras and Lie triple data.
📌 3 Key Takeaways
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Objective & Hypothesis:We introduce the notion of a generalized metric $n$-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric $n$-Leibniz algebras and faithful generalized orthogonal representations of metric Lie algebras (called Lie triple datas).
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Key Findings & Data:We introduce the notion of a generalized metric $n$-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric $n$-Leibniz algebras and faithful generalized orthogonal representations of metric Lie algebras (called Lie triple datas).
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Conclusion & Impact:We further show that there is also a one-to-one correspondence between generalized orthogonal derivations (resp. generalized orthogonal automorphisms) on generalized metric $n$-Leibniz algebras and Lie triple data.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Generalized metric $n$-Leibniz algebra · metric Lie algebra · generalized orthogonal representation
Abstract
We introduce the notion of a generalized metric $n$-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric $n$-Leibniz algebras and faithful generalized orthogonal representations of metric Lie algebras (called Lie triple datas). We further show that there is also a one-to-one correspondence between generalized orthogonal derivations (resp. generalized orthogonal automorphisms) on generalized metric $n$-Leibniz algebras and Lie triple data.
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Cite This Article
TANG, R., SONG, L. (2018). Generalized metric $n$-Leibniz algebras and generalized orthogonal representation of metric Lie algebras. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 6, 3061–3077. https://ajindex.com/articles/227819