Book Review: Determinantal rings
نویسندگان
چکیده
منابع مشابه
Initial Algebras of Determinantal Rings
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 کاملDeterminantal Varieties over Truncated Polynomial Rings
We study higher order determinantal varieties obtained by considering generic m × n (m ≤ n) matrices over rings of the form F [t]/(t k), and for some fixed r, setting the coefficients of powers of t of all r × r minors to zero. These varieties can be interpreted as generalized tangent bundles over the classical deter-minantal varieties; a special case of these varieties first appeared in a prob...
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 کاملPrime 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 ...
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: Bulletin of the American Mathematical Society
سال: 1990
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1990-15911-7