Ideals in hom-associative Weyl algebras

Year 2025, Volume: 38 Issue: 38, 74 - 81, 14.07.2025

Per Back Johan Richter

https://doi.org/10.24330/ieja.1587178

Cited By: 1

Abstract

We introduce hom-associative versions of the higher order Weyl algebras, generalizing the construction of the first hom-associative Weyl algebras. We then show that the higher order hom-associative Weyl algebras are simple, and that all their one-sided ideals are principal.

Keywords

Hom-associative Weyl algebra , hom-associative Ore extension , Stafford’s theorem

References

• P. Back and J. Richter, On the hom-associative Weyl algebras, J. Pure Appl. Algebra, 224(9) (2020), 106368 (12 pp).
• P. Back and J. Richter, The hom-associative Weyl algebras in prime characteristic, Int. Electron. J. Algebra, 31 (2022), 203-229.
• P. Back, J. Richter and S. Silvestrov, Hom-associative Ore extensions and weak unitalizations, Int. Electron. J. Algebra, 24 (2018), 174-194.
• J. Dixmier, Sur les algebres de Weyl, Bull. Soc. Math. France, 96 (1968), 209-242.
• J. Dixmier, Sur les algebres de Weyl II, Bull. Sci. Math., 94 (1970), 289-301.
• Y. Fregier and A. Gohr, On unitality conditions for Hom-associative algebras, arXiv:0904.4874 [math.RA] (2009).
• J. T. Hartwig, D. Larsson and S. D. Silvestrov, Deformations of Lie algebras using $\sigma$-derivations, J. Algebra, 295(2) (2006), 314-361.
• A. Makhlouf and S. D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl., 2(2) (2008), 51-64.
• J. T. Stafford, Completely faithful modules and ideals of simple Noetherian rings, Bull. London Math. Soc., 8(2) (1976), 168-173.
• J. T. Stafford, Module structure of Weyl algebras, J. London Math. Soc., 18(3) (1978), 429-442.
• D. Yau, Hom-algebras and homology, J. Lie Theory, 19(2) (2009), 409-421.