Prime ideals in certain quantum determinantal rings
| dc.creator | Goodearl, K. R. | |
| dc.creator | Lenagan, T. H. | |
| dc.date | 1999-03-24 | |
| dc.date.accessioned | 2026-07-07T05:28:27Z | |
| dc.date.available | 2026-07-07T05:28:27Z | |
| dc.description | The ideal I generated by the 2x2 quantum minors in the algebra A = O_q(M_{m,n}(k)) (the quantized coordinate algebra of mxn matrices) is investigated. Analogues of the First and Second Fundamental Theorems of Invariant Theory are proved. In particular, it is shown that I is a completely prime ideal, that is, A/I is an integral domain, and that A/I is the ring of coinvariants of a coaction of k[x,x^{-1}] on O_q(k^m) tensor O_q(k^n), a tensor product of two quantum affine spaces. (That the ideal of A generated by the txt quantum minors, for any t, is completely prime is proved in the authors' paper `Quantum determinantal ideals'.) There is a natural torus action on A/I induced by an (m+n)-torus action on A. We identify the invariant prime ideals for this action and deduce consequences for the prime spectrum of A/I. | |
| dc.description | 13 pages, to appear in Proceedings of Euroconference on Interactions between Ring Theory and Representations of Algebras (Murcia, 1998). See also http://www.math.ucsb.edu/~goodearl/preprints.html/ | |
| dc.identifier | https://arxiv.org/abs/math/9903143 | |
| dc.identifier | http://arxiv.org/abs/math/9903143 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78264 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16D30, 17B37 | |
| dc.title | Prime ideals in certain quantum determinantal rings | |
| dc.type | text |