Following the definition given in [6], we compute the ring of quantum differential operators on the polynomial ring in 1 variable. We further study this ring.
Ž. In 1988, J. Bernstein and V. Lunts In¨ent. Math. 94, 223᎐243 proved that a generic surface in ސ 3 of degree 4 or greater would not contain a curve which supported a module over the second Weyl algebra. It is known that quadric surfaces and planes always do. This paper shows that a generic cubic surface does not. ᮊ
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