Tohoku Mathematical Journal

Primitive ideals of the ring of differential operators on an affine toric variety

Mutsumi Saito

Full-text: Open access

Abstract

We show that the classification of $A$-hypergeometric systems and that of multi-graded simple modules (up to shift) over the ring of differential operators on an affine toric variety are the same. We then show that the set of multi-homogeneous primitive ideals of the ring of differential operators is finite. Furthermore, we give conditions for the algebra being simple.

Article information

Source
Tohoku Math. J. (2), Volume 59, Number 1 (2007), 119-144.

Dates
First available in Project Euclid: 16 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1176734751

Digital Object Identifier
doi:10.2748/tmj/1176734751

Mathematical Reviews number (MathSciNet)
MR2321996

Zentralblatt MATH identifier
1162.13305

Subjects
Primary: 13N10: Rings of differential operators and their modules [See also 16S32, 32C38]
Secondary: 13P99: None of the above, but in this section 16W35 16S32: Rings of differential operators [See also 13N10, 32C38]

Keywords
Primitive ideals toric variety ring of differential operators hypergeometric systems

Citation

Saito, Mutsumi. Primitive ideals of the ring of differential operators on an affine toric variety. Tohoku Math. J. (2) 59 (2007), no. 1, 119--144. doi:10.2748/tmj/1176734751. https://projecteuclid.org/euclid.tmj/1176734751


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