A Remark on the Dixmier Conjecture

DOI10.4153/S0008439519000122zbMath1441.16027arXiv1812.00042WikidataQ123197931 ScholiaQ123197931MaRDI QIDQ5215641

Viktor Levandovskyy, Vladimir V. Bavula

Publication date: 12 February 2020

Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.00042

zbMATH Keywords

automorphismWeyl algebraendomorphismDixmier conjecturea \(\mathbb{Z}\)-graded algebra

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Automorphisms and endomorphisms (16W20) Graded rings and modules (associative rings and algebras) (16W50) Rings of differential operators (associative algebraic aspects) (16S32)

Cites Work

• Unnamed Item
• Finite dimensionality of \(\text{Ext}^ n\)'s and \(\text{Tor}_ n\)'s of simple modules over one class of algebras
• Dixmier's problem 5 for the Weyl algebra.
• The Jacobian Conjecture\(_{2n}\) implies the Dixmier Problem\(_n\)
• An analogue of the conjecture of Dixmier is true for the algebra of polynomial integro-differential operators.
• Endomorphisms of Weyl algebra and \(p\)-curvatures.
• A proof of the equivalence of the Dixmier, Jacobian and Poisson conjectures
• The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
• The Weyl Algebra-Semisimple and Nilpotent Elements
• Sur les algèbres de Weyl
• A question of Rentschler and the Dixmier problem

This page was built for publication: A Remark on the Dixmier Conjecture