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