Corpus ID: 195798659

# The universal enveloping algebra of $\mathfrak{sl}_2$ and the Racah algebra

title={The universal enveloping algebra of \$\mathfrak\{sl\}_2\$ and the Racah algebra},
Let $\mathbb{F}$ denote a field with ${\rm char\,}\mathbb{F}\not=2$. The Racah algebra $\Re$ is the unital associative $\mathbb{F}$-algebra defined by generators and relations in the following way. The generators are $A$, $B$, $C$, $D$. The relations assert that \begin{equation*} [A,B]=[B,C]=[C,A]=2D \end{equation*} and each of the elements \begin{gather*} \alpha=[A,D]+AC-BA, \qquad \beta=[B,D]+BA-CB, \qquad \gamma=[C,D]+CB-AC \end{gather*} is central in $\Re$. Additionally the element \$\delta… Expand