Quantum differential operators on K[x]

Details Quantum differential operators on K[x] Quantum differential operators on K[x]

2000-10-04

arxiv.org/abs/math/0010041v3

Mathematics

Quantum Algebra

26 pages, references added. To appear in International Journal of Mathematics

Scientific paper

Following the definition of quantum differential operators given by Lunts and Rosenberg in (Sel. math., New ser. 3 (1997) 335--359), we show that the ring of quantum differential operators on the affine line is the ring generated by x and \del, the familiar differential operators on the line, along with two additional operators which we call \del^\beta^1 and \del^\beta^-1. We describe this ring both as a subring of the ring of graded endomorphisms and as a ring given by generators and relations. From this starting point, we are able to describe the ring of quantum differential operators on affine n-space and to construct the ring of global quantum differential operators on the projective line.

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