Notes for AKT-091008-2/0:21:16

PBW theorem: Choose an ordered basis $x_{1},\cdots ,x_{n}$ of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{G}} , then $U({\mathcal {G}})$ is the vector space with basis being all monotone non-decreasing words in $x_{1},\cdots ,x_{n}$