英和和英

名詞

quasicentroid (複数形 quasicentroids)

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   • 2016, Ruipu Bai, Qiyong Li, Kai Zhang, “Generalized derivations of ${\displaystyle 3}$-Lie algebras”, in arXiv^[1]:

     The main results are: for all ${\displaystyle 3}$-Lie algebra ${\displaystyle A}$, 1) the generalized derivation algebra ${\displaystyle GDer(A)}$ is the sum of quasiderivation algebra ${\displaystyle QDer(A)}$ and quasicentroid ${\displaystyle Q\Gamma (A)}$; 2) quasiderivations of ${\displaystyle A}$ can be embedded as derivations in a larger algebra; 3) quasiderivation algebra ${\displaystyle QDer(A)}$ normalizer quasicentroid, that is, ${\displaystyle [QDer(A),Q\Gamma (A)]\subseteq Q\Gamma (A)}$; 4) if ${\displaystyle A}$ contains a maximal diagonalized tours ${\displaystyle T}$, then ${\displaystyle QDer(A)}$ and ${\displaystyle Q\Gamma (A)}$ are diagonalized ${\displaystyle T}$-modules, that is, as ${\displaystyle T}$-modules, ${\displaystyle (T,T)}$ semi-simplely acts on ${\displaystyle QDer(A)}$ and ${\displaystyle Q\Gamma (A)}$, respectively..