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Journals / International Electronic Journal of Algebra / 2014 / Cilt: 15 - Sayı: 15

CENTRALIZERS IN ORE EXTENSIONS OF POLYNOMIAL RINGS

Johan RİCHTER
Sergei SİLVESTROV
Pages
196–207
Publication Date
2014-06-01
DOI
—
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We also show that for certain classes of elements their centralizer is singly generated as an algebra.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we consider centralizers of single elements in certain Ore extensions, with a non-invertible endomorphism, of the ring of polynomials in one variable over a field.
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Key Findings & Data:We show that they are commutative and finitely generated as algebras.
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Conclusion & Impact:We also show that for certain classes of elements their centralizer is singly generated as an algebra.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ore extension · centralizer

Abstract

In this paper, we consider centralizers of single elements in certain Ore extensions, with a non-invertible endomorphism, of the ring of polynomials in one variable over a field. We show that they are commutative and finitely generated as algebras. We also show that for certain classes of elements their centralizer is singly generated as an algebra.

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Cite This Article

RİCHTER, J., SİLVESTROV, S. (2014). CENTRALIZERS IN ORE EXTENSIONS OF POLYNOMIAL RINGS. International Electronic Journal of Algebra, Cilt: 15 - Sayı: 15, 196–207. https://ajindex.com/articles/832432

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References (7)

  1. S. A. Amitsur, Commutative linear differential operators, Pacific J. Math. 8 (1958), 1–10.
  2. D. Arnal and G. Pinczon, On algebraically irreducible representations of the Lie algebra sl(2), J. Math. Phys., 15 (1974), 350–359.
  3. V. V. Bavula, Generalized Weyl algebras and their representations, Algebra i Analiz, 4(1) (1992), 75–97; translation in: St. Petersburg Math. J., 4(1), –92. J. P. Bell and L. W. Small, Centralizers in domains of Gelfand-Kirillov dimen- sion 2, Bull. Lond. Math. Soc., 36(6) (2004), 779–785.
  4. R. C. Carlson and K. R. Goodearl, Commutants of ordinary differential oper- ators, J. Differential Equations, 35(3) (1980), 339–365.
  5. J. Dixmier, Sur les alg`ebres de Weyl, Bull. Soc. Math. France, 96 (1968), 209– K. R. Goodearl, Centralizers in differential, pseudodifferential, and fractional differential operator rings, Rocky Mountain J. Math., 13(4) (1983), 573–618.
  6. K. R. Goodearl and R. B. Warfield, An introduction to noncommutative Noe- therian rings, second ed., London Mathematical Society Student Texts, vol. 61, Cambridge University Press, Cambridge, 2004. L. Hellstr¨om and S. D. Silvestrov, Ergodipotent maps and commutativity of elements in noncommutative rings and algebras with twisted intertwining, J. Algebra, 314(1) (2007), 17–41.
  7. L. Makar-Limanov, Centralizers in the quantum plane algebra, Studies in Lie theory, Progr. Math., vol. 243, Birkh¨auser Boston, Boston, MA, 2006, pp. 411– J. Richter, Burchnall-Chaundy theory for Ore extensions, Proceedings of the AGMP, Springer-Verlag, (to appear). X. Tang, Maximal commutative subalgebras of certain skew polynomial rings, Johan Richter Centre for Mathematical Sciences Lund University Box 118, SE-22199 Lund, Sweden e-mail: [email protected] Sergei Silvestrov Division of Applied Mathematics The School of Education, Culture and Communication M¨alardalen University Box 883, SE-72123 V¨aster˚as, Sweden e-mail: [email protected]