Prime ideals in certain quantum determinantal rings

dc.creatorGoodearl, K. R.
dc.creatorLenagan, T. H.
dc.date1999-03-24
dc.date.accessioned2026-07-07T05:28:27Z
dc.date.available2026-07-07T05:28:27Z
dc.descriptionThe 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.description13 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.identifierhttps://arxiv.org/abs/math/9903143
dc.identifierhttp://arxiv.org/abs/math/9903143
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78264
dc.subjectQuantum Algebra
dc.subjectRings and Algebras
dc.subject16D30, 17B37
dc.titlePrime ideals in certain quantum determinantal rings
dc.typetext

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