quasiderivation

quasiderivation

English

Etymology

quasi- +‎ derivation

Noun

quasiderivation (plural quasiderivations)

1. (mathematics) This term needs a definition. Please help out and add a definition, then remove the text {{rfdef}}.
   • 2016, Ruipu Bai, Qiyong Li, Kai Zhang, “Generalized derivations of ${\\displaystyle 3}$-Lie algebras”, in arXiv‎:

     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..