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 $k[P]$.References
- Jacques Dixmier, Sur les algèbres de Weyl, Bull. Soc. Math. France 96 (1968), 209–242 (French). MR 242897
- V. V. Bavula, Dixmier’s Problem 5 for the Weyl algebra, J. Algebra 283 (2005), no. 2, 604–621. MR 2111212, DOI 10.1016/j.jalgebra.2004.09.013
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