What does $\mathfrak {aff}$ mean in $\mathfrak{aff}(1)=\{\begin{pmatrix} a&b \\ 0&0 \end{pmatrix}\,:\,a,b\in\mathbb{R}\}$? I am reading this Wikipedia article about the possible two-dimensional Lie-algebras:

What does $\mathfrak {aff}$ mean here?
 A: The affine group $\mathrm{Aff}(V)$ of a vector space is the group of affine transformations $x\mapsto Ax+b$ (where $A\in\mathrm{End}(V)$ and $b\in V$). We write $\mathrm{Aff}(n,F)$ or $\mathrm{Aff}_nF$ if $V=F^n$ over a field $F$.
It is tradition to use the lowercase fraktur letter for a lie algebra corresponding to the usual capital letter for the Lie group (e.g. $\frak g$ vs. $G$). In particular, $\mathfrak{aff}(V)$ would denote the lie algebra of $\mathrm{Aff}(V)$.
There is a canonical way to embed $\mathrm{Aff}(V)$ into $\mathrm{GL}(V\oplus F)$, namely as the setwise stabilizer of $V\times\{1\}$, which can be described using block matrices:
$$ (x\mapsto Ax+b) \quad\longleftrightarrow\quad \begin{bmatrix} A & b \\ 0 & 1\end{bmatrix} $$
If we assume $A(t)$ and $b(t)$ are differentiable functions of $t$ yielding the identity matrix in $\mathrm{GL}(n+1,F)$ at $t=0$, we can differentiate and evaluate at $t=0$ to get the general form of an element of the lie algebra $\mathfrak{aff}(n,F)$: its elements have bottom row all $0$.
