Launois, Stephane
*
Generators for H-invariant prime ideals in O-q(M-m,M-p(C)).
*
Proceedings of The Edinburgh Mathematical Society,
47
(1).
pp. 163-190.
ISSN 0013-0915.
(doi:https://doi.org/10.1017/S001309150200718)
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Official URL http://dx.doi.org/10.1017/S0013091502000718 |

## Abstract

It is known that, for generic q, the H-invariant prime ideals in O-q(M-m,M-p(C)) are generated by quantum minors (see S. Launois, Les ideaux premiers invariants de O-q(M-m,M-p(C)), J. Alg., in press). In this paper, m and p being given, we construct an algorithm which computes a generating set of quantum minors for each H-invariant prime ideal in O-q(M-m,M-p(C)). We also describe, in the general case, an explicit generating set of quantum minors for some particular H-invariant prime ideals in O-q(M-m,M-p(C)). In particular, if (Y-i,Y-alpha)((i,alpha)is an element of[1,m]x[1,p]) denotes the matrix of the canonical generators of O-q(M-m,M-p(C)), we prove that, if u greater than or equal to 3, the ideal in O-q(M-m,M-p(C)) generated by Y-1,Y-p and the u x u quantum minors is prime. This result allows Lenagan and Rigal to show that the quantum determinantal factor rings of O-q(M-m,M-p(C)) are maximal orders (see T. H. Lenagan and L.

Item Type: | Article |
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Uncontrolled keywords: | quantum matrices; quantum minors; prime ideals; quantum determinantal ideals; deleting-derivations algorithms |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Stephane Launois |

Date Deposited: | 24 Sep 2008 16:41 UTC |

Last Modified: | 28 May 2014 10:57 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/7407 (The current URI for this page, for reference purposes) |

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