[Une nouvelle famille d’algèbres dont les schémas de représentations sont lisses]
Dans cet article, nous fournissons une condition nécéssaire et suffisante pour la lissité du schéma qui paramétrise les représentations -dimensionelles d’une algèbre associative, engendrée par un nombre fini d’éléments sur un corps algébriquement clos. En particulier, notre résultat implique que les points satisfaisant sont réguliers. Ceci généralise aux algèbres engendrées par un nombre fini d’éléments des résultats connus sur les algèbres de dimension finie.
We give a necessary and sufficient smoothness condition for the scheme parameterizing the -dimensional representations of a finitely generated associative algebra over an algebraically closed field. In particular, our result implies that the points satisfying are regular. This generalizes well-known results on finite-dimensional algebras to finitely generated algebras.
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Keywords: Noncommutative Geometry, Hochschild Cohomology, Representation Theory
Mot clés : Géométrie non-commutative, cohomologie de Hochschild, théorie des Représentations
Ardizzoni, Alessandro 1 ; Galluzzi, Federica 1 ; Vaccarino, Francesco 2, 3
@article{AIF_2016__66_3_1261_0,
author = {Ardizzoni, Alessandro and Galluzzi, Federica and Vaccarino, Francesco},
title = {A new family of algebras whose representation schemes are smooth},
journal = {Annales de l'Institut Fourier},
pages = {1261--1277},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {3},
year = {2016},
doi = {10.5802/aif.3037},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3037/}
}
TY - JOUR AU - Ardizzoni, Alessandro AU - Galluzzi, Federica AU - Vaccarino, Francesco TI - A new family of algebras whose representation schemes are smooth JO - Annales de l'Institut Fourier PY - 2016 SP - 1261 EP - 1277 VL - 66 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3037/ DO - 10.5802/aif.3037 LA - en ID - AIF_2016__66_3_1261_0 ER -
%0 Journal Article %A Ardizzoni, Alessandro %A Galluzzi, Federica %A Vaccarino, Francesco %T A new family of algebras whose representation schemes are smooth %J Annales de l'Institut Fourier %D 2016 %P 1261-1277 %V 66 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3037/ %R 10.5802/aif.3037 %G en %F AIF_2016__66_3_1261_0
Ardizzoni, Alessandro; Galluzzi, Federica; Vaccarino, Francesco. A new family of algebras whose representation schemes are smooth. Annales de l'Institut Fourier, Tome 66 (2016) no. 3, pp. 1261-1277. doi : 10.5802/aif.3037. https://aif.centre-mersenne.org/articles/10.5802/aif.3037/
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