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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  1. Luchezar L. Avramov, Srikanth Iyengar, Gaps in Hochschild cohomology imply smoothness for commutative algebras, Math. Res. Lett. 12 (2005), 789-804 Zbl1101.13018MR2189239
  2. Luchezar L. Avramov, Micheline Vigué-Poirrier, Hochschild homology criteria for smoothness, Internat. Math. Res. Notices (1992), 17-25 Zbl0755.13006MR1149001
  3. BACH, A Hochschild homology criterium for the smoothness of an algebra, Comment. Math. Helv. 69 (1994), 163-168 Zbl0824.13009MR1282365
  4. V. V. Bavula, Generalized Weyl algebras and their representations, Algebra i Analiz 4 (1992), 75-97 Zbl0807.16027MR1171955
  5. Vladimir Bavula, Global dimension of generalized Weyl algebras, Representation theory of algebras (Cocoyoc, 1994) 18 (1996), 81-107, Amer. Math. Soc., Providence, RI Zbl0857.16025MR1388045
  6. Petter Andreas Bergh, Karin Erdmann, Homology and cohomology of quantum complete intersections, Algebra Number Theory 2 (2008), 501-522 Zbl1205.16011MR2429451
  7. Petter Andreas Bergh, Dag Madsen, Hochschild homology and global dimension, Bull. Lond. Math. Soc. 41 (2009), 473-482 Zbl1207.16006MR2506831
  8. Ragnar-Olaf Buchweitz, Edward L. Green, Dag Madsen, Øyvind Solberg, Finite Hochschild cohomology without finite global dimension, Math. Res. Lett. 12 (2005), 805-816 Zbl1138.16003MR2189240
  9. M. A. Farinati, A. Solotar, M. Suárez-Álvarez, Hochschild homology and cohomology of generalized Weyl algebras, Ann. Inst. Fourier (Grenoble) 53 (2003), 465-488 Zbl1100.16008MR1990004
  10. Yang Han, Hochschild (co)homology dimension, J. London Math. Soc. (2) 73 (2006), 657-668 Zbl1139.16010MR2241972
  11. Dieter Happel, Hochschild cohomology of finite-dimensional algebras, Séminaire d’Algèbre Paul Dubreil et Marie-Paul Malliavin, 39ème Année (Paris, 1987/1988) 1404 (1989), 108-126, Springer, Berlin Zbl0688.16033MR1035222
  12. G. Hochschild, Bertram Kostant, Alex Rosenberg, Differential forms on regular affine algebras, Trans. Amer. Math. Soc. 102 (1962), 383-408 Zbl0102.27701MR142598
  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
  15. Antonio G. Rodicio, Commutative augmented algebras with two vanishing homology modules, Adv. Math. 111 (1995), 162-165 Zbl0830.13011MR1317386
  16. S. P. Smith, A class of algebras similar to the enveloping algebra of sl ( 2 ) , Trans. Amer. Math. Soc. 322 (1990), 285-314 Zbl0732.16019MR972706
  17. Andrea Solotar, Micheline Vigué-Poirrier, Two classes of algebras with infinite Hochschild homology, Proc. Amer. Math. Soc. 138 (2010), 861-869 Zbl1227.16011MR2566552

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