PRIME IDEALS IN CERTAIN QUANTUM DETERMINANTAL RINGS K. R. Goodearl and T. H. Lenagan
نویسنده
چکیده
The ideal I1 generated by the 2× 2 quantum minors in the coordinate algebra of quantum matrices, Oq(Mm,n(k)), is investigated. Analogues of the First and Second Fundamental Theorems of Invariant Theory are proved. In particular, it is shown that I1 is a completely prime ideal, that is, Oq(Mm,n(k))/I1 is an integral domain, and that Oq(Mm,n(k))/I1 is the ring of coinvariants of a coaction of k[x, x] on Oq(km)⊗Oq(kn), a tensor product of two quantum affine spaces. There is a natural torus action on Oq(Mm,n(k))/I1 induced by an (m + n)-torus action on Oq(Mm,n(k)). We identify the invariant prime ideals for this action and deduce consequences for the prime spectrum of Oq(Mm,n(k))/I1.
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