Hochschild homology and cohomology of generalized Weyl algebras

Marco A. Farinati[1]; Andrea L. Solotar[1]; Mariano Suárez-Álvarez[1]

  • [1] Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentine)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 2, page 465-488
  • ISSN: 0373-0956

Abstract

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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 ( 𝔰 𝔩 2 ) , primitive quotients of 𝒰 ( 𝔰 𝔩 2 ) , 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 generators 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

How to cite

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Farinati, Marco A., Solotar, Andrea L., and Suárez-Álvarez, Mariano. "Hochschild homology and cohomology of generalized Weyl algebras." Annales de l’institut Fourier 53.2 (2003): 465-488. <http://eudml.org/doc/116043>.

@article{Farinati2003,
abstract = {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, $\{\mathcal \{U\}\}(\{\mathfrak \{s\}\}\{\mathfrak \{l\}\}_2)$, primitive quotients of $\{\mathcal \{U\}\}(\{\mathfrak \{s\}\}\{\mathfrak \{l\}\}_2)$, 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 generators 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},
affiliation = {Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentine); Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentine); Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentine)},
author = {Farinati, Marco A., Solotar, Andrea L., Suárez-Álvarez, Mariano},
journal = {Annales de l’institut Fourier},
keywords = {Hochschild cohomology; generalized Weyl algebras; automorphism group; algebras of invariants; automorphism groups; skew polynomial extensions},
language = {eng},
number = {2},
pages = {465-488},
publisher = {Association des Annales de l'Institut Fourier},
title = {Hochschild homology and cohomology of generalized Weyl algebras},
url = {http://eudml.org/doc/116043},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Farinati, Marco A.
AU - Solotar, Andrea L.
AU - Suárez-Álvarez, Mariano
TI - Hochschild homology and cohomology of generalized Weyl algebras
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 2
SP - 465
EP - 488
AB - 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, ${\mathcal {U}}({\mathfrak {s}}{\mathfrak {l}}_2)$, primitive quotients of ${\mathcal {U}}({\mathfrak {s}}{\mathfrak {l}}_2)$, 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 generators 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
LA - eng
KW - Hochschild cohomology; generalized Weyl algebras; automorphism group; algebras of invariants; automorphism groups; skew polynomial extensions
UR - http://eudml.org/doc/116043
ER -

References

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