منابع مشابه
Prime Ideals in Certain Quantum Determinantal Rings
The ideal I 1 generated by the 2 2 quantum minors in the coordinate algebra of quantum matrices, O q (M m;n (k)), is investigated. Analogues of the First and Second Fundamental Theorems of Invariant Theory are proved. In particular, it is shown that I 1 is a completely prime ideal, that is, O q (M m;n (k))=I 1 is an integral domain, and that O q (M m;n (k))=I 1 is the ring of coinvariants of a ...
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We develop a method of reducing the size of quantum minors in the algebra of quantum matrices Oq(Mn). We use the method to show that the quantum determinantal factor rings of Oq(Mn(C)) are maximal orders, for q an element of C transcendental over Q. 2000 Mathematics subject classification: 16P40, 16W35, 20G42.
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We study initial algebras of determinantal rings, defined by minors of generic matrices, with respect to their classical generic point. This approach leads to very short proofs for the structural properties of determinantal rings. Moreover, it allows us to classify their Cohen-Macaulay and Ulrich ideals.
متن کاملF-Rationality of Determinantal Rings and Their Rees Rings
Let X be an m × n matrix (m ≤ n) of indeterminates over a field K of positive characteristic, and denote the ideal generated by its t-minors by It . We show that the Rees ringR(It ) ofK[X], as well as the algebra At generated by the t-minors, are F-rational if charK > min(t, m − t). Without a restriction on characteristic this holds for K[X]/Ir+1 and the symbolic Rees ring R(It ). The determina...
متن کاملRepresentations of Braid Groups via Determinantal Rings
We construct representations for braid groups Bn via actions of Bn on a determinantal ring, thus mirroring the setting of the classical representation theory for GLn. The representations that we construct fix a certain unitary form.
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2002
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089502020098