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On the hom-associative Weyl algebras
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-6309-8709
Blekinge Tekniska Högskola.ORCID iD: 0000-0003-3931-7358
2020 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 224, no 9Article in journal (Refereed) Published
Abstract [en]

The first (associative) Weyl algebra is formally rigid in the classical sense. In this paper, we show that it can however be formally deformed in a nontrivial way when considered as a so-called hom-associative algebra, and that this deformation preserves properties such as the commuter, while deforming others, such as the center, power associativity, the set of derivations, and some commutation relations. We then show that this deformation induces a formal deformation of the corresponding Lie algebra into what is known as a hom-Lie algebra, when using the commutator as bracket. We also prove that all homomorphisms between any two purely hom-associative Weyl algebras are in fact isomorphisms. In particular, all endomorphisms are automorphisms in this case, hence proving a hom-associative analogue of the Dixmier conjecture to hold true.

Place, publisher, year, edition, pages
2020. Vol. 224, no 9
Keywords [en]
Dixmier conjecture, hom-associative Ore extensions, hom-associative Weyl algebras, formal hom-associative deformations, formal hom-Lie deformations
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-47517DOI: 10.1016/j.jpaa.2020.106368OAI: oai:DiVA.org:mdh-47517DiVA, id: diva2:1423638
Available from: 2020-04-15 Created: 2020-04-15 Last updated: 2020-04-17Bibliographically approved

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Bäck, Per

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