Quantized symplectic oscillator algebras of rank one

DOI10.1016/J.JALGEBRA.2006.06.051zbMath1194.17003arXivmath/0405176OpenAlexW2009873750MaRDI QIDQ875922

Wee Liang Gan, Apoorva Khare

Publication date: 16 April 2007

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

Full work available at URL: https://arxiv.org/abs/math/0405176

zbMATH Keywords

quantizationcategory \(\mathcal O\)symplectic reflection algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (7)

Cleft extensions of Koszul twisted Calabi-Yau algebras ⋮ Center and Representations of Infinitesimal Hecke Algebras of 𝔰𝔩₂ ⋮ The category of weight modules for symplectic oscillator Lie algebras ⋮ The prime spectrum of the algebra \(\mathbb{K}_q[X,Y \rtimes U_q(\mathfrak{sl}_2)\) and a classification of simple weight modules] ⋮ Category \(\mathcal O\) over a deformation of the symplectic oscillator algebra. ⋮ Functoriality of the BGG Category 𝒪†† ⋮ BGG CATEGORY FOR THE QUANTUM SCHRÖDINGER ALGEBRA

Cites Work

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• Biinvertible actions of Hopf algebras
• Continuous Hecke algebras.
• The diamond lemma for ring theory
• Category of \(\mathfrak g\) modules
• Lectures on algebraic quantum groups
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Category \(\mathcal O\) over a deformation of the symplectic oscillator algebra.
• Noncommutative deformations of Kleinian singularities

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