Let π = ( c 1 , β¦ , c d - 1 ) β β d - 1 π subscript π 1 normal-β¦ subscript π π 1 superscript β π 1 \mathbf{c}=(c_{1},\ldots,c_{d-1})\in\mathbb{C}^{d-1} bold_c = ( italic_c start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , β¦ , italic_c start_POSTSUBSCRIPT italic_d - 1 end_POSTSUBSCRIPT ) β blackboard_C start_POSTSUPERSCRIPT italic_d - 1 end_POSTSUPERSCRIPT . The rational Cherednik algebra π§ t , π β’ ( Ξ ) subscript π§ π‘ π normal-Ξ \mathsf{H}_{t,\mathbf{c}}(\Gamma) sansserif_H start_POSTSUBSCRIPT italic_t , bold_c end_POSTSUBSCRIPT ( roman_Ξ ) of rank one is the algebra generated by elements u , v , Ξ³ π’ π£ πΎ u,v,\gamma italic_u , italic_v , italic_Ξ³ with Ξ³ β Ξ = β€ / d β’ β€ πΎ normal-Ξ β€ π β€ \gamma\in\Gamma=\mathbb{Z}/d\mathbb{Z} italic_Ξ³ β roman_Ξ = blackboard_Z / italic_d blackboard_Z and the following relations: