= Weyl deformation of a polynomial algebra in two variables
{c}
{title2=$yx-xy=t$}
The algebra over $k[t]$ defined by $yx-xy=t$ has ordered <basis> $x^iy^j$, by its differential Ore-extension construction. Its $t$-adic completion is a formal associative <formal associative deformation> of $k[x,y]$. In characteristic zero its first-order multiplication term is $f(a,b)=\partial_y a\,\partial_x b$. The cocycle is not a coboundary: a degree-two coboundary on a commutative algebra is symmetric, whereas $f(y,x)-f(x,y)=1$.
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