A classification of 𝐻-primes of quantum partial flag varieties

DOI10.1090/S0002-9939-09-10180-6zbMath1245.16030arXiv0910.0997OpenAlexW2964184174MaRDI QIDQ3552116

Milen T. Yakimov

Publication date: 13 April 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.0997

zbMATH Keywords

quantized universal enveloping algebrasstratificationsquantized coordinate ringscompletely prime idealsinvariant prime idealsLie algebras of algebraic groupsquantum partial flag varietiessimply connected split semisimple algebraic groups

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Grassmannians, Schubert varieties, flag manifolds (14M15) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Quantum groups (quantized function algebras) and their representations (20G42) Lie algebras of linear algebraic groups (17B45) Ideals in associative algebras (16D25) Ring-theoretic aspects of quantum groups (16T20)

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Cites Work

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• Poisson structures on affine spaces and flag varieties. I: Matrix affine Poisson space.
• Closure relations for totally nonnegative cells in \(G/P\)
• Prime ideals in the quantum Grassmannian.
• On the quantum flag manifold
• Primitive ideals of \(\mathbb{C}_ q[SL(n)\)]
• Semiprime and prime crossed products
• The prime and the primitive spectra of a quantum Bruhat cell translate
• Admissible diagrams in quantum nilpotent algebras and combinatoric properties of Weyl groups
• Invariant prime ideals in quantizations of nilpotent Lie algebras
• Poisson structures on affine spaces and flag varieties. II
• The Dixmier-Moeglin equivalence in quantum coordinate rings and quantized Weyl algebras
• Introduction to quantum groups