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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the centralizers in the Weyl algebra
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by Jorge A. Guccione, Juan J. Guccione and Christian Valqui PDF
Proc. Amer. Math. Soc. 140 (2012), 1233-1241 Request permission

Abstract:

Let $P,Q$ be elements of the Weyl algebra $W$. We prove that if $[Q,P]=1$, then the centralizer of $P$ is the polynomial algebra $k[P]$.
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Additional Information
  • Jorge A. Guccione
  • Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria-Pabellón 1, (C1428EGA) Buenos Aires, Argentina
  • Email: vander@dm.uba.ar
  • Juan J. Guccione
  • Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria-Pabellón 1, (C1428EGA) Buenos Aires, Argentina
  • Email: jjgucci@dm.uba.ar
  • Christian Valqui
  • Affiliation: Pontificia Universidad Católica del Perú, Instituto de Matemática y Ciencias Afines, Sección Matemáticas, PUCP, Av. Universitaria 1801, San Miguel, Lima 32, Perú
  • Email: cvalqui@pucp.edu.pe
  • Received by editor(s): March 30, 2010
  • Received by editor(s) in revised form: January 5, 2011
  • Published electronically: August 12, 2011
  • Additional Notes: The first author was supported by UBACYT 095, PIP 112-200801-00900 (CONICET) and PUCP-DAI-2009-0042
    The second author was supported by UBACYT 095, PICT 2006 00836 (FONCYT) and PIP 112-200801-00900 (CONICET). He is thankful for the appointment as a visiting professor “Cátedra José Tola Pasquel” and for the hospitality during his stay at the PUCP
    The third author was supported by PUCP-DAI-2009-0042, Lucet 90-DAI-L005, SFB 478 U. Münster, Konrad Adenauer Stiftung.
  • Communicated by: Harm Derksen
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1233-1241
  • MSC (2010): Primary 16S32
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11017-7
  • MathSciNet review: 2869108