Prime spectrum of \(O_q(M_n(k))\): canonical image and normal separation

DOI10.1016/S0021-8693(02)00543-4zbMath1024.16001OpenAlexW2461108372MaRDI QIDQ1868764

Gérard Cauchon

Publication date: 28 April 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-8693(02)00543-4

zbMATH Keywords

prime idealsprime spectracoordinate algebras of quantum matricesalgebras of regular functionsquantum affine spaces

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Quantum groups (quantized function algebras) and their representations (20G42) Ideals in associative algebras (16D25) Ring-theoretic aspects of quantum groups (16T20)

Related Items (31)

Real spectra of quantum groups ⋮ Primitive ideals and automorphisms of quantum matrices. ⋮ The prime spectrum and simple modules over the quantum spatial ageing algebra ⋮ Combinatorics of \(\mathcal H\)-primes in quantum matrices ⋮ Basic quadratic identities on quantum minors ⋮ From Grassmann necklaces to restricted permutations and back again ⋮ Totally nonnegative cells and matrix Poisson varieties ⋮ Total Positivity is a Quantum Phenomenon: The Grassmannian Case ⋮ Efficient recognition of totally nonnegative matrix cells ⋮ The Launois-Lenagan conjecture. ⋮ Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves. ⋮ Enumeration of \(\mathcal H\)-strata in quantum matrices with respect to dimension ⋮ The invariant prime ideals of \(O_q({\mathcal M}_{m,p}(\mathbb{C}))\). ⋮ Quantum Schubert cells via representation theory and ring theory ⋮ RATIONAL GROUP ACTIONS ON AFFINE PI-ALGEBRAS ⋮ SPECTRA AND CATENARITY OF MULTI-PARAMETER QUANTUM SCHUBERT CELLS ⋮ Prime factors of quantum Schubert cell algebras and clusters for quantum Richardson varieties ⋮ Connected quantized Weyl algebras and quantum cluster algebras ⋮ Further applications of the Cauchon algorithm to rank determination and bidiagonal factorization ⋮ Quantized matrix algebras and quantum seeds ⋮ A graph theoretic method for determining generating sets of prime ideals in quantum matrices ⋮ Cauchon diagrams for quantized enveloping algebras ⋮ RANKtℋ-PRIMES IN QUANTUM MATRICES ⋮ On universal quadratic identities for minors of quantum matrices ⋮ On universal quadratic identities for minors of quantum matrices ⋮ AN ALGORITHM TO CONSTRUCT THE LE DIAGRAM ASSOCIATED TO A GRASSMANN NECKLACE ⋮ Admissible diagrams in quantum nilpotent algebras and combinatoric properties of Weyl groups ⋮ Dimension and enumeration of primitive ideals in quantum algebras. ⋮ Tauvel’s height formula for quantum nilpotent algebras ⋮ An automaton-theoretic approach to the representation theory of quantum algebras ⋮ Catenarity in quantum nilpotent algebras

Cites Work

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• Determinants of matrices over noncommutative rings
• Vanishing of derivations and prime spectra of quantum algebras
• Prime quotients of \(O_ q({\mathfrak m}_ n(k))\)
• Catenarity in quantum algebras
• The quantum coordinate ring of the special linear group
• Quantum deformations of GL_n
• The Dixmier-Moeglin equivalence in quantum coordinate rings and quantized Weyl algebras
• Prime spectra of quantum semisimple groups
• Quantum linear groups

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