My question os motivated, naturally, by the problem of classifying symplectic reflection algebras up to Morita equivalence (a classical reference for rational Cherednik algebras is **Y. Berest, P. Etingof, V. Ginzburg**, *"Morita equivalence of Cherednik algebras"*, **MR2034924**; the most up do date work in this subject I know of is **I. Losev**, *Derived equivalences for Symplectic reflection algebras*, https://arxiv.org/abs/1704.05144);

and also the problem of understading rings of differential operators on irreducilbe affine complex varieties $X$ up to Morita equivalence (a nice discussion of this lovely problem in the intersection of ring theory and algebraic geometry can be found in **Y. Berest, G. Wilson**, *"Differential isomorphism and equivalence of algebraic varieties"*, **MR2079372**)

Given that, my questions are:

**(Question 1):** What are the more general known conditions on a symplectic reflection algebra $H_{1,c}(V,\Gamma)$ that imples it is Morita equivalent to $\mathcal{D}(V) \rtimes \Gamma$?

**(Question 2):** What are the recent developments made in the study of equivalence of rings of differential operators up to Morita equivalence (and in particular Morita equivalent to the Weyl algebra) since **Berest, Wilson [op. cit.]**?

**(Question 3):** Etingof in *"Cherednik and Hecke algebras of varieties with a finite group action"*, **MR3734656**, introduces more general versions of rational Cherednik algebras and discuss the possibility of extending the results in **Y. Berest, O. Chalykh**, *Quasi-invariants of complex reflection groups* ,**MR 2801407**, in this setting. So, being optmistic, one hipothetically could obtain results similar as those discussed in **Berest, Etingof, Ginzburg [op. cit]** regarding Morita equivalence of these generalized rational Cherednik algebras with smash products of rings with differential operatos with a finite groups. Has this line of inquiry lead to results relevant to this discussion so far?

**(Question 4):** This is totally unrelated to the previous questions. It is more of a very open question in ring theory: are there interesting simple Noetherian algebras, coming from another areas than those above, which are Morita equivalent to a Weyl algebra or a smash product of it with a finite group?