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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
In this work, it is proven that every normal automorphism of $\mathfrak{M}$ is an IA-automorphism and the group of normal automorphisms coincides with the group of inner automorphisms.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Let $\mathfrak{M}$ be a free metabelian Leibniz algebra generating set $X=\{x_{1},...,x_{n}\}$ over the field $\mathfrak{K}$ of characteristic $0$.
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Temel Bulgular & Veri:An automorphism $ \phi $ of $\mathfrak{M}$ is said to be normal automorphism if each ideal of $\mathfrak{M}$ is invariant under $ \phi $.
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Sonuç & Katkı:In this work, it is proven that every normal automorphism of $\mathfrak{M}$ is an IA-automorphism and the group of normal automorphisms coincides with the group of inner automorphisms.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Leibniz algebra · normal automorphism · inner automorphism
Abstract
Let $\mathfrak{M}$ be a free metabelian Leibniz algebra generating set $X=\{x_{1},...,x_{n}\}$ over the field $\mathfrak{K}$ of characteristic $0$. An automorphism $ \phi $ of $\mathfrak{M}$ is said to be normal automorphism if each ideal of $\mathfrak{M}$ is invariant under $ \phi $. In this work, it is proven that every normal automorphism of $\mathfrak{M}$ is an IA-automorphism and the group of normal automorphisms coincides with the group of inner automorphisms.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
Özkurt, Z. Y. (2024). Normal automorphisms of free metabelian Leibniz algebras. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 1. https://doi.org/10.31801/cfsuasmas.1265768