Classifications of prime ideals and simple modules of the Weyl algebra \(A_1\) in prime characteristic

DOI10.3836/tjm/1502179377OpenAlexW4312998036MaRDI QIDQ6116785

Vladimir V. Bavula

Publication date: 18 July 2023

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/tokyo-journal-of-mathematics/volume-46/issue-1/Classifications-of-Prime-Ideals-and-Simple-Modules-of-the-Weyl/10.3836/tjm/1502179377.full

zbMATH Keywords

normGalois groupWeyl algebramaximal idealprime idealsimple moduleskew polynomial ringdivision algebraprimitive idealcyclic algebracompletely prime idealskew Laurent polynomial ring

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Automorphisms and endomorphisms (16W20) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Rings of differential operators (associative algebraic aspects) (16S32) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Ideals in associative algebras (16D25) Finite-dimensional division rings (16K20)

Cites Work

• The prime spectrum and simple modules over the quantum spatial ageing algebra
• The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra
• Endomorphisms of Weyl algebra and \(p\)-curvatures.
• Simple D[X, Y; ?,a-modules]
• THE GROUP OF AUTOMORPHISMS OF THE FIRST WEYL ALGEBRA IN PRIME CHARACTERISTIC AND THE RESTRICTION MAP
• The simple modules of the ore extensions with coefficients from a dedekind ring
• On automorphisms of Weyl algebra
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