A parametric family of subalgebras of the Weyl algebra I. Structure and automorphisms

DOI10.1090/S0002-9947-2014-06144-8zbMath1312.16020arXiv1210.4631MaRDI QIDQ5496654

Matthew Ondrus, Samuel A. Lopes, Georgia M. Benkart

Publication date: 2 February 2015

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

Full work available at URL: https://arxiv.org/abs/1210.4631

zbMATH Keywords

automorphism groupsquantum Weyl algebrasdifferential operatorsalgebras of invariantsOre extensionsquantum planes

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Automorphisms and endomorphisms (16W20) Rings of differential operators (associative algebraic aspects) (16S32)

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Cites Work

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• From quantum Ore extensions to quantum tori via noncommutative UFDs
• On normal subgroups of \(\Aut_k(A_1(k))\), the \(k\)-automorphisms group of Weyl algebra \(A_1(k)\).
• The Jordan plane over a field of positive characteristic.
• On the field of fractions of certain quantum algebras
• The simple modules of certain generalized crossed products
• Noncommutative graded domains with quadratic growth
• Endomorphisms of Weyl algebra and \(p\)-curvatures.
• Derivations of a parametric family of subalgebras of the Weyl algebra.
• Jordanian plane.
• Derivations of Ore Extensions of the Polynomial Ring in One Variable
• Non-commutative unique factorization domains
• Hopf quivers and Nichols algebras in positive characteristic
• Non-Commutative Unique Factorisation Rings
• Noetherian Ore Extensions and Jacobson Rings
• Examples in non-commutative projective geometry
• Invariants du corps de weyl sous l'action de groupes finis
• Isomorphism problems and groups of automorphisms for generalized Weyl algebras
• Endomorphisms of Right Ideals of the Weyl Algebra
• A Parametric Family of Subalgebras of the Weyl Algebra II. Irreducible Modules
• On automorphisms of Weyl algebra
• Two-Generated Algebras and Standard-Form Congruence
• Representation Spaces of the Jordan Plane
• ISOMORPHISMS BETWEEN QUANTUM GENERALIZED WEYL ALGEBRAS
• Sur les algèbres de Weyl

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