Lecture Notes on Bayesian Estimation and Classification
《Lecture Notes on Bayesian Estimation and Classification》 · 第 314 页 · Chapter 11，Section 11.1「Group Extensions and Covering Groups」，小节「Inner Derivations」
Let us now assume that $N$ is abelian, so that $N$ is a $G$-module. We shall write $A$ instead of $N$. […] If $a\in A$, we define a function $\delta(a):G\to A$ by the rule $g^{\delta(a)}=[g,a]=a^{-g+1}$. The commutator identity $[g_1g_2,a]=[g_1,a]^{g_2}[g_2,a]$ tells us at once that $\delta(a)$ is a derivation. Such derivations are called inner (or $1$-coboundaries), the subset of inner derivations being written $\operatorname{Inn}(G,A)$ or $B^1(G,A)$.