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Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case

Andrea Solotar[1]; Mariano Suárez-Alvarez[1]; Quimey Vivas[1]

  • [1] Departamento de Matemática-IMAS Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1 1428, Buenos Aires, Argentina.

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 3, page 923-956
  • ISSN: 0373-0956

Abstract

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We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of ‘quantum’ type in all but a few exceptional cases.

How to cite

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Solotar, Andrea, Suárez-Alvarez, Mariano, and Vivas, Quimey. "Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case." Annales de l’institut Fourier 63.3 (2013): 923-956. <http://eudml.org/doc/275669>.

@article{Solotar2013,
abstract = {We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of ‘quantum’ type in all but a few exceptional cases.},
affiliation = {Departamento de Matemática-IMAS Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1 1428, Buenos Aires, Argentina.; Departamento de Matemática-IMAS Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1 1428, Buenos Aires, Argentina.; Departamento de Matemática-IMAS Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1 1428, Buenos Aires, Argentina.},
author = {Solotar, Andrea, Suárez-Alvarez, Mariano, Vivas, Quimey},
journal = {Annales de l’institut Fourier},
keywords = {generalized Weyl algebra; Hochschild cohomology; global dimension; generalized Weyl algebras; Hochschild homology},
language = {eng},
number = {3},
pages = {923-956},
publisher = {Association des Annales de l’institut Fourier},
title = {Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case},
url = {http://eudml.org/doc/275669},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Solotar, Andrea
AU - Suárez-Alvarez, Mariano
AU - Vivas, Quimey
TI - Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 3
SP - 923
EP - 956
AB - We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of ‘quantum’ type in all but a few exceptional cases.
LA - eng
KW - generalized Weyl algebra; Hochschild cohomology; global dimension; generalized Weyl algebras; Hochschild homology
UR - http://eudml.org/doc/275669
ER -

References

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  10. Yang Han, Hochschild (co)homology dimension, J. London Math. Soc. (2) 73 (2006), 657-668 Zbl1139.16010MR2241972
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  13. Lionel Richard, Andrea Solotar, Isomorphisms between quantum generalized Weyl algebras, J. Algebra Appl. 5 (2006), 271-285 Zbl1102.16025MR2235811
  14. Antonio G. Rodicio, Smooth algebras and vanishing of Hochschild homology, Comment. Math. Helv. 65 (1990), 474-477 Zbl0726.13008MR1069822
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