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On the hom-associat...
On the hom-associative Weyl algebras
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- Bäck, Per, 1987- (författare)
- Mälardalens högskola,Utbildningsvetenskap och Matematik,MAM,Mälardalen University, SWE
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- Richter, Johan, 1986- (författare)
- Blekinge Tekniska Högskola,Institutionen för matematik och naturvetenskap
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(creator_code:org_t)
- Elsevier BV, 2020
- 2020
- Engelska.
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Ingår i: Journal of Pure and Applied Algebra. - : Elsevier BV. - 0022-4049 .- 1873-1376. ; 224:9
- Relaterad länk:
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http://arxiv.org/pdf...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
Nyckelord
- Dixmier conjecture
- hom-associative Ore extensions
- hom-associative Weyl algebras
- formal hom-associative deformations
- formal hom-Lie deformations
- Mathematics/Applied Mathematics
- matematik/tillämpad matematik
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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