$\newcommand{\RR}{\mathbb{R}} \newcommand{\CC}{\mathbb{C}} \newcommand{\NN}{\mathbb{N}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\freecarnot}[1]{F_{#1}} \newcommand{\freelie}[1]{\mathfrak{f}_{#1}} \newcommand{\lielayer}[2]{#1^{[#2]}} \newcommand{\freelielayer}[2]{\lielayer{\freelie{#1}}{#2}} \newcommand{\lowercentralseriesterm}[2]{\lielayer{#1}{\geq #2}} \newcommand{\abnormalpolynomial}[2]{P_{#1}^{#2}} \newcommand{\Ad}[1]{\operatorname{Ad}_{#1}} \newcommand{\ad}[1]{\operatorname{ad}_{#1}} \newcommand{\abs}[1]{\left\vert #1\right\vert} \newcommand{\freelieaction}{D} \newcommand{\acts}{\curvearrowright} \newcommand{\into}{\hookrightarrow} \newcommand{\identity}[1]{e} \newcommand{\hallset}{\mathcal{H}} \newcommand{\polyring}[1]{\RR[#1]} \newcommand{\fractionfield}[1]{\RR(#1)} \newcommand{\polyringextended}[2]{\fractionfield{#1}[#2]} \newcommand{\covector}{\lambda} \newcommand{\covectorb}{\eta} \newcommand{\differenceinteger}[1]{C_{#1}} \newcommand{\poincare}{P} \newcommand{\vectorparam}[1]{\boldsymbol{#1}} \newcommand{\freeparam}{\alpha} \newcommand{\factorpolynomial}[1]{S^{#1}} \newcommand{\factorcoefficient}[1]{\nu_{#1}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&}$