Hochschild homology and cohomology of generalized Weyl algebras

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We compute Hochschild homology and cohomology of a class of generalized Weyl algebras, introduced by V. V. Bavula in St. Petersbourg Math. Journal, 4 (1) (1999), 71-90. Examples of such algebras are the n-th Weyl algebras, U(sl2). primitive quotients of U(sl2), and subalgebras of invariants of these...

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Autor principal: Farinati, M.A
Otros Autores: Solotar, A., Suárez-Álvarez, M.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Association des Annales de l'Institut Fourier 2003
Acceso en línea:Registro en Scopus
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100 1 |a Farinati, M.A. 
245 1 0 |a Hochschild homology and cohomology of generalized Weyl algebras 
260 |b Association des Annales de l'Institut Fourier  |c 2003 
270 1 0 |m Suárez-Álvarez, M.; Universidad de Buenos Aires, Fac. de Ciencias Exactas y Naturales, Dpto de Matemática, Ciudad Universitaria Pab I (1428), Buenos Aires, Argentina; email: mariano@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Alev, J., Farinati, M., Lambre, T., Solotar, A., Homologie des invariants d'une algèbre de Weyl sous l'action d'un groupe fini (2000) J. of Alg., 232 (2), pp. 564-577 
504 |a Alev, J., Lambre, T., Comparaison de l'homologie de hochschild et de l'homologie de Poisson pour une déformation des surfaces de Klein (1998) Algebra and Operator Theory, Proceedings of the Colloquium, pp. 25-38. , Tashkent: Kluwer Academic publishers 
504 |a Alev, J., Lambre, T., Homologie des invariants d'une algèbre de Weyl (1999) K-Theory, 18, pp. 401-411 
504 |a Bavula, V., Generalized Weyl algebras and their representations (1990) St. Petersbourg Math. J., 4 (1), pp. 71-90 
504 |a Bavula, V., Jordan, D., Isomorphism problems and groups automorphisms for generalized Weyl algebras (2001) Trans. Am. Math. Soc., 353 (2), pp. 769-794 
504 |a Bavula, V., Lenagan, T., Krull dimension of generalized Weyl algebras with noncommutative coefficients (2001) J. of Alg., 235 (1), pp. 315-358 
504 |a Burghelea, D., Vigué-Poirrier, M., Cyclic homology of commutative algebras, I (1988) Springer Lecture Notes in Math., 1318, pp. 51-72 
504 |a Cartan, H., Eilenberg, S., (1956) Homological Algebra, , Princeton, Princeton Univ. Press 
504 |a Dixmier, J., Quotients simples de l'algèbre enveloppante de sl2 (1973) J. of Alg., 24, pp. 551-574 
504 |a Etingof, P., Ginzburg, V., Symplectic Reflection Algebras, Calogero-Moser Spaces, and Deformed Harish-Chandra Homomorphism, , Preprint, arXiv:math.AG/0011114 v5 
504 |a Fleury, O., (1997) Automorphismes d'Algèbres Enveloppantes Classiques et Quantifiées : Sous-groupes Finis et Invariants, , Thèse Université de Reims, Champagne-Ardenne 
504 |a Fleury, O., Sur les invariants de Bλ sous l'action de sous-groupes finis d'automorphismes: Conjecture de Gelfand - Kirillov et homologie de Hochschild (2001) Comm. in Alg., 29 (8), pp. 3535-3557 
504 |a Hodges, T.J., Noncommutative deformations of type-A Kleinian singularities (1993) J. Algebra, 161 (2), pp. 271-290 
504 |a Kassel, C., L'homologie cyclique des algèbres enveloppantes (1988) Invent. Math., 91 (2), pp. 221-251 
504 |a Kassel, C., Vigué-Poirrier, M., Homologie des quotients primitifs de l'algèbre enveloppante de sl2 (1992) Math. Ann., 294 (3), pp. 483-502 
504 |a Smith, S., A class of algebras similar to the enveloping algebra of sl2 (1990) Trans. Am. Math. Soc., 322 (1), pp. 285-314 
504 |a Springer, T.A., Invariant theory (1977) Lecture Notes in Mathematics, 585. , Berlin-Heidelberg-New York: Springer-Verlag 
504 |a Sridharan, R., Filtered algebras and representations of Lie algebras (1961) Trans. Am. Math. Soc., 100, pp. 530-550 
504 |a Ştefan, D., Hochschild cohomology on Hopf-Galois extensions (1995) J. Pure Appl. Alg., 103 (2), pp. 221-233 
504 |a Suárez-Álvarez, M., Multiplicative structure of Hochschild cohomology of the ring of invariants of a Weyl algebra under finite groups J. of Alg. 
504 |a Suárez-Álvarez, M., Hochschild Cohomology of Primitive Quotients of U(sl2) and Their Rings of Invariants, , http://www.math.jussieu.fr/~mariano 
504 |a Van Den Bergh, M., A relation between Hochschild homology and cohomology for Gorenstein rings (1998) Proc. Am. Math. Soc., 126 (5), pp. 1345-1348 
504 |a Van Den Bergh, M., A Relation Between Hochschild Homology and Cohomology for Gorenstein Rings, , Erratum, to appear 
520 3 |a We compute Hochschild homology and cohomology of a class of generalized Weyl algebras, introduced by V. V. Bavula in St. Petersbourg Math. Journal, 4 (1) (1999), 71-90. Examples of such algebras are the n-th Weyl algebras, U(sl2). primitive quotients of U(sl2), and subalgebras of invariants of these algebras under finite cyclic groups of automorphisms. We answer a question of Bavula-Jordan (Trans. A.M.S., 353 (2) (2001), 769-794) concerning the generatore of the group of automorphisms of a generalized Weyl algebra. We also explain previous results on the invariants of Weyl algebras and of primitive quotients.  |l eng 
593 |a Universidad de Buenos Aires, Fac. de Ciencias Exactas y Naturales, Dpto de Matemática, Ciudad Universitaria Pab I (1428), Buenos Aires, Argentina 
690 1 0 |a AUTOMORPHISM GROUP 
690 1 0 |a GENERALIZED WEYL ALGEBRAS 
690 1 0 |a HOCHSCHILD HOMOLOGY 
700 1 |a Solotar, A. 
700 1 |a Suárez-Álvarez, M. 
773 0 |d Association des Annales de l'Institut Fourier, 2003  |g v. 53  |h pp. 465-488+VI+X  |k n. 2  |p Ann. Inst. Fourier  |x 03730956  |w (AR-BaUEN)CENRE-239  |t Annales de l'Institut Fourier 
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