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In this review paper we show how the Cherednik algebra of type$\check{C_1}C_1$ appears naturally as quantisation of the group algebra of themonodromy group associated to the sixth Painlev\'e equation. This factnaturally leads to an embedding of the Cherednik algebra of type$\check{C_1}C_1$ into $Mat(2,\mathbb T_q)$, i.e. $2\times 2$ matrices withentries in the quantum torus. For $q=1$ this result is equivalent to say thatthe Cherednik algebra of type $\check{C_1}C_1$ is Azumaya of degree $2$\cite{O}. By quantising the action of the braid group and of the Okamototransformations on the monodromy group associated to the sixth Painlev\'eequation we study the automorphisms of the Cherednik algebra of type$\check{C_1}C_1$ and conjecture the existence of a new automorphism. Inspiredby the confluences of the Painlev\'e equations, we produce similar embeddingsfor the confluent Cherednik algebras $\mathcal H_V,\mathcal H_{IV},\mathcalH_{III},\mathcal H_{II}$ and $\mathcal H_{I},$ defined in arXiv:1307.6140.

Embedding of the rank 1 DAHA into Mat(2,Tq) and its automorphisms