RING THEORETIC PROPERTIES OF QUANTUM GRASSMANNIANS

DOI10.1142/S0219498804000630zbMath1081.16048arXivmath/0208152MaRDI QIDQ5315536

A. C. Kelly, Laurent Rigal, Thomas H. Lenagan

Publication date: 8 September 2005

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0208152

zbMATH Keywords

quantum groupsquantum matricesmaximal orderscoinvariantsquantum Grassmanniansquantum determinantsnoncommutative dehomogenisation

Mathematics Subject Classification ID

Related Items (20)

Algebraic properties of Manin matrices. I ⋮ Double-partition quantum cluster algebras ⋮ Quantum graded algebras with a straightening law and the AS-Cohen-Macaulay property for quantum determinantal rings and quantum Grassmannians. ⋮ Graded quantum cluster algebras and an application to quantum Grassmannians ⋮ Categorification and the quantum Grassmannian ⋮ Total Positivity is a Quantum Phenomenon: The Grassmannian Case ⋮ A Borel-Weil theorem for the quantum Grassmannians ⋮ The automorphism group of the quantum grassmannian ⋮ Transfer results for Frobenius extensions ⋮ The AS-Cohen-Macaulay property for quantum flag manifolds of minuscule weight ⋮ AUTOMORPHISMS OF QUANTUM MATRICES ⋮ A quantum analogue of the dihedral action on Grassmannians. ⋮ Examples of quantum cluster algebras associated to partial flag varieties. ⋮ Quantum cluster algebra structures on quantum nilpotent algebras ⋮ Quantum- and quasi-Plücker coordinates. ⋮ QUASI-DETERMINANTS AND q-COMMUTING MINORS ⋮ QUANTUM ANALOGUES OF SCHUBERT VARIETIES IN THE GRASSMANNIAN ⋮ Twisting the quantum grassmannian ⋮ Two-Parameter Analogs of the Heisenberg Enveloping Algebra ⋮ GENERALISED QUANTUM DETERMINANTAL RINGS ARE MAXIMAL ORDERS

Cites Work

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• Quantum deformation of the Grassmannian manifold
• Connected graded Gorenstein algebras with enough normal elements
• The first fundamental theorem of coinvariant theory for the quantum general linear group
• A DEFORMATION OF THE BIG CELL INSIDE THE GRASSMANNIAN MANIFOLD G(r,n)
• Quantum coinvariant theory for the quantum special linear group and quantum Schubert varieties

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