PRIME IDEALS INVARIANT UNDER WINDING AUTOMORPHISMS IN QUANTUM MATRICES

DOI10.1142/S0129167X02001393zbMath1054.16030arXivmath/0110072MaRDI QIDQ4807409

Thomas H. Lenagan, Kenneth R. Goodearl

Publication date: 18 May 2003

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0110072

zbMATH Keywords

prime idealsquantum minorsprime spectraquantized coordinate algebrasquantized upper triangular matrices

Mathematics Subject Classification ID

Rings arising from noncommutative algebraic geometry (16S38) Endomorphism rings; matrix rings (16S50) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Automorphisms and endomorphisms (16W20) Quantum groups (quantized function algebras) and their representations (20G42) Ideals in associative algebras (16D25)

Related Items (14)

Poisson structures on affine spaces and flag varieties. I: Matrix affine Poisson space. ⋮ Irreducible representations of quantum solvable algebras at roots of 1 ⋮ Combinatorics of \(\mathcal H\)-primes in quantum matrices ⋮ Quantized coordinate rings of the unipotent radicals of the standard Borel subgroups in \(\mathrm{SL}_{n+1}\). ⋮ Total Positivity is a Quantum Phenomenon: The Grassmannian Case ⋮ LU decomposition of totally nonnegative matrices ⋮ Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules ⋮ Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves. ⋮ The invariant prime ideals of \(O_q({\mathcal M}_{m,p}(\mathbb{C}))\). ⋮ Transfer results for Frobenius extensions ⋮ A graph theoretic method for determining generating sets of prime ideals in quantum matrices ⋮ RANKtℋ-PRIMES IN QUANTUM MATRICES ⋮ GENERALISED QUANTUM DETERMINANTAL RINGS ARE MAXIMAL ORDERS ⋮ Winding-invariant prime ideals in quantum \(3\times 3\) matrices.

Cites Work

• Actions of algebraic groups on the spectrum of rational ideals. II
• Primitive ideals of \({\mathbf C}_ q[SL(3)\)]
• Primitive ideals of \(\mathbb{C}_ q[SL(n)\)]
• Quantum function algebra at roots of 1
• Quantum determinantal ideals
• The quantum coordinate ring of the special linear group
• Orbites d'un groupe algébrique dans l'espace des idéaux rationnels d'une algèbre enveloppante
• The Dixmier-Moeglin equivalence in quantum coordinate rings and quantized Weyl algebras

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