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Quantum differential operators on K[x]

Uma N. Iyer·Timothy C. McCune
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Abstract

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^β^1 and \del^β^-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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BibTeXRIS

Uma N. Iyer, Timothy C. McCune. 2002-01-12. Quantum differential operators on K[x]. https://arxiv.org/abs/math/0010041

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