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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. © Association des Annales de l'institut Fourier, 2013.

Registro:

Documento: Artículo
Título:Hochschild homology and cohomology of generalized weyl algebras: The quantum case
Autor:Solotar, A.; Suárez-Alvarez, M.; Vivas, Q.
Filiación:Departamento de Matemática-IMAS, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, 1428, Buenos Aires, Argentina
Palabras clave:Generalized Weyl algebra; Global dimension; Hochschild cohomology
Año:2013
Volumen:63
Número:3
Página de inicio:923
Página de fin:956
DOI: http://dx.doi.org/10.5802/aif.2780
Título revista:Annales de l'Institut Fourier
Título revista abreviado:Ann. Inst. Fourier
ISSN:03730956
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03730956_v63_n3_p923_Solotar

Referencias:

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  • A Hochschild homology criterium for the smoothness of an algebra (1994) Comment. Math. Helv, 69 (2), pp. 163-168
  • Bavula, V.V., Generalized Weyl algebras and their representations (1992) Algebra i Analiz, 4 (1), pp. 75-97
  • Bavula, V., Global dimension of generalized Weyl algebras (1996) CMS Conf. Proc, 18, pp. 81-107. , Representation theory of algebras (Cocoyoc, 1994), Amer. Math. Soc., Providence, R.I
  • Bergh, P.A., Erdmann, K., Homology and cohomology of quantum complete intersections (2008) Algebra Number Theory, 2 (5), pp. 501-522
  • Bergh, P.A., Madsen, D., Hochschild homology and global dimension (2009) Bull. Lond. Math. Soc, 41 (3), pp. 473-482
  • Buchweitz, R.-O., Green, E.L., Madsen, D., Solberg Ø, Finite Hochschild cohomology without finite global dimension (2005) Math. Res. Lett, 12 (5-6), pp. 805-816
  • Farinati, M.A., Solotar, A., Suárez-Álvarez, M., Hochschild homology and cohomology of generalized Weyl algebras (2003) Ann. Inst. Fourier (Grenoble), 53 (2), pp. 465-488
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  • Happel, D., Hochschild cohomology of finite-dimensional algebras (1989) Lecture Notes in Math, 1404, pp. 108-126. , Séminaire d'Algèbre Paul Dubreil et Marie-Paul Malliavin 39ème Année (Paris, 1987/1988) Springer, Berlin
  • Hochschild, G., Kostant, B., Rosenberg, A., Differential forms on regular affine algebras (1962) Trans. Amer. Math. Soc, 102, pp. 383-408
  • Richard, L., Solotar, A., Isomorphisms between quantum generalized Weyl algebras (2006) J. Algebra Appl, 5 (3), pp. 271-285
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  • Solotar, A., Vigué-Poirrier, M., Two classes of algebras with infinite Hochschild homology (2010) Proc. Amer. Math. Soc, 138 (3), pp. 861-869

Citas:

---------- APA ----------
Solotar, A., Suárez-Alvarez, M. & Vivas, Q. (2013) . Hochschild homology and cohomology of generalized weyl algebras: The quantum case. Annales de l'Institut Fourier, 63(3), 923-956.
http://dx.doi.org/10.5802/aif.2780
---------- CHICAGO ----------
Solotar, A., Suárez-Alvarez, M., Vivas, Q. "Hochschild homology and cohomology of generalized weyl algebras: The quantum case" . Annales de l'Institut Fourier 63, no. 3 (2013) : 923-956.
http://dx.doi.org/10.5802/aif.2780
---------- MLA ----------
Solotar, A., Suárez-Alvarez, M., Vivas, Q. "Hochschild homology and cohomology of generalized weyl algebras: The quantum case" . Annales de l'Institut Fourier, vol. 63, no. 3, 2013, pp. 923-956.
http://dx.doi.org/10.5802/aif.2780
---------- VANCOUVER ----------
Solotar, A., Suárez-Alvarez, M., Vivas, Q. Hochschild homology and cohomology of generalized weyl algebras: The quantum case. Ann. Inst. Fourier. 2013;63(3):923-956.
http://dx.doi.org/10.5802/aif.2780