Automorphisms of quantum polynomial rings and Drinfeld Hecke algebras

DOI10.4171/jncg/568MaRDI QIDQ6594003

Anne Shepler, Christine Uhl

Publication date: 27 August 2024

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

zbMATH Keywords

automorphism groupsdeformationsskew polynomial ringquantum determinantquantum polynomial ringsDrinfeld Hecke algebra

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Ordinary and skew polynomial rings and semigroup rings (16S36) Automorphisms and endomorphisms (16W20) Deformations of associative rings (16S80) Twisted and skew group rings, crossed products (16S35)

Cites Work

• Discriminant formulas and applications
• The discriminant controls automorphism groups of noncommutative algebras.
• Some remarks on Koszul algebras and quantum groups
• Hochschild cohomology and quantum Drinfeld Hecke algebras
• Algebraic properties of Manin matrices. I
• Cuspidal local systems and graded Hecke algebras. I
• Shephard-Todd-Chevalley theorem for skew polynomial rings.
• Quantum polynomial algebras
• On the trace of graded automorphisms
• Classification of graded Hecke algebras for complex reflection groups.
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Discriminants and automorphism groups of Veronese subrings of skew polynomial rings
• Determinants of matrices over noncommutative rings
• Deformations of quantum symmetric algebras extended by groups.
• Gorensteinness of invariant subrings of quantum algebras
• Noncommutative deformations of Kleinian singularities
• Noncommutative Dunkl operators and braided Cherednik algebras.
• Mystic reflection groups.
• Automorphisms and isomorphisms of quantum generalized Weyl algebras.
• PBW deformations of quantum symmetric algebras and their group extensions.
• Quantum Drinfeld Hecke Algebras
• Hochschild cohomology of group extensions of quantum symmetric algebras
• Affine Hecke Algebras and Their Graded Version
• Hochschild cohomology and graded Hecke algebras
• Derivations et automorphismes de quelques algebras quantiques
• Noncommutative Auslander theorem
• Quantum Drinfeld Orbifold Algebras
• Rigidité des plongements des quotients primitifs minimaux de U_g(sl(2)) dans l’algebre quantique de Weyl-Hayashi
• Finite Unitary Reflection Groups
• Homological properties of quantum polynomials

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