An explicit injective homomorphism embeds the Racah algebra into F[a,b,c] ⊗ U(sl_2) using equitable generators of U(sl_2), proving the Racah algebra is a domain.
Terwilliger, The universal Askey-Wilson algebra and the equitable prese ntation of Uq(sl2), SIGMA Symmetry Integrability Geom
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The universal enveloping algebra of $\mathfrak{sl}_2$ and the Racah algebra
An explicit injective homomorphism embeds the Racah algebra into F[a,b,c] ⊗ U(sl_2) using equitable generators of U(sl_2), proving the Racah algebra is a domain.