Solution of a \(q\)-difference Noether problem and the quantum Gelfand-Kirillov conjecture for \(\mathfrak{gl}_N\)

DOI10.1007/s00209-013-1184-3zbMath1297.17010arXiv1111.6044OpenAlexW2029836197WikidataQ122891013 ScholiaQ122891013MaRDI QIDQ2636969

Jonas T. Hartwig, Vyacheslav M. Futorny

Publication date: 18 February 2014

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.6044

zbMATH Keywords

Gelfand-Kirillov conjectureinvariantNoether problemqauntum groupskew field of fraction

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Universal enveloping (super)algebras (17B35) Ring-theoretic aspects of quantum groups (16T20)

Related Items

Quantum groups, quantum tori, and the Grothendieck-Springer resolution, De Concini-Kac filtration and Gelfand-Tsetlin generators for quantum \(\mathfrak{gl}_N\), Generic Gelfand-Tsetlin modules of quantized and classical orthogonal algebras, Construction of representations of Poincaré group using Lie fields, An extension of \(U( \mathfrak{gl}_n)\) related to the alternating group and Galois orders, Some aspects of noncommutative invariant theory and the Noether's problem, Principal Galois orders and Gelfand-Zeitlin modules, \textit{LD}-stability for Goldie rings, Homogeneous localizations of some quantum enveloping superalgebras, Quantum linear Galois orders

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Modular Lie algebras and the Gelfand-Kirillov conjecture
• Galois orders in skew monoid rings.
• Quantum group invariants and link polynomials
• Primideale in Einhüllenden auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume)
• Quantization of the Dixmier localization of \(U(sl_{n+1}(\mathbb C))\)
• Rings of skew polynomials and Gel'fand-Kirillov conjecture for quantum groups
• On the field of fractions of certain quantum algebras
• The Gelfand-Kirillov conjecture for Lie algebras of dimension at most eight
• Lectures on algebraic quantum groups
• Gelfand-Zetlin basis for \(U_ q(\mathfrak{gl}(\text{\textbf{N}}+\text{\textbf{1}}))\) modules.
• Vanishing of derivations and prime spectra of quantum algebras
• A simple localization of the quantized Weyl algebra
• The skew field of rational functions on \(\text{GL}_ q(n,K)\)
• Sur les corps liés aux algèbres enveloppantes des algèbres de Lie
• The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite \(W\)-algebras
• The Isomorphism Question for Division Rings of Group Rings
• Proof of the Gelfand-Kirillov Conjecture for Solvable Lie Algebras
• Representations of Solvable Lie Algebras and the Gelfand-Kirillov Conjecture
• SUR LES ENDOMORPHISMES DES TORES QUANTIQUES
• A class of counterexamples to the Gel’fand-Kirillov conjecture
• On the Gelfand-Kirillov conjecture for quantum algebras
• Shorter Notes: The Field of Multisymmetric Functions
• Invariants of Certain Groups I
• The quantum Casimir operators of {\rm {U}}_q{(\mathfrak {gl}_{n})} and their eigenvalues
• Fields of fractions of quantum solvable algebras
• On Gelfand-Zetlin modules over \(U_q(gl_n)\)