Fields of fractions of quantum solvable algebras

DOI10.1006/jabr.2000.8463zbMath0966.17008arXivmath/9906060OpenAlexW2060843697MaRDI QIDQ5929444

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Publication date: 14 August 2001

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

Full work available at URL: https://arxiv.org/abs/math/9906060

zbMATH Keywords

enveloping algebrafields of fractionsGelfand-Kirillov conjecturequantum algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Universal enveloping (super)algebras (17B35) Solvable, nilpotent (super)algebras (17B30)

Related Items (12)

SUR LES ENDOMORPHISMES DES TORES QUANTIQUES ⋮ Solution of a \(q\)-difference Noether problem and the quantum Gelfand-Kirillov conjecture for \(\mathfrak{gl}_N\) ⋮ Irreducible representations of quantum solvable algebras at roots of 1 ⋮ Projective modules and Gröbner bases for skew PBW extensions ⋮ Hochschild homology and cohomology of some classical and quantum noncommutative polynomial algebras. ⋮ Theq-difference Noether problem for complex reflection groups and quantum OGZ algebras ⋮ PI degree parity in \(q\)-skew polynomial rings. ⋮ ORE AND GOLDIE THEOREMS FOR SKEW PBW EXTENSIONS ⋮ Large commutative subalgebras of quantum algebras. ⋮ STRATIFICATION OF PRIME SPECTRUM OF QUANTUM SOLVABLE ALGEBRAS ⋮ Rational equivalence of classical and quantum polynomial algebras. ⋮ Vanishing of derivations and prime spectra of quantum algebras

Cites Work

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• Quantum groups at roots of 1
• On the \(q\)-commutations in \(U_q({\mathfrak n})\) at roots of one
• On the field of fractions of certain quantum algebras
• Prime quotients of \(O_ q({\mathfrak m}_ n(k))\)
• Prime ideals in skew and 𝑞-skew polynomial rings
• Division rings of quotients and central elements of multiparameter quantizations
• On the Gelfand-Kirillov conjecture for quantum algebras

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