Polynomial representation of the Heisenberg Lie algebra
= Polynomial representation of the Heisenberg Lie algebra
{c}
On $\mathbb C[x]$, the operators $d/dx$, multiplication by $x$, and the identity satisfy $[d/dx,x]=1$. Sending $a,b,c$ to these operators gives a faithful irreducible infinite-dimensional representation of the <Heisenberg Lie algebra>.