A new family of algebras whose representation schemes are smooth
Annales de l'Institut Fourier, Volume 66 (2016) no. 3, p. 1261-1277

We give a necessary and sufficient smoothness condition for the scheme parameterizing the n-dimensional representations of a finitely generated associative algebra over an algebraically closed field. In particular, our result implies that the points MRep A n (k) satisfying Ext A 2 (M,M)=0 are regular. This generalizes well-known results on finite-dimensional algebras to finitely generated algebras.

Dans cet article, nous fournissons une condition nécéssaire et suffisante pour la lissité du schéma qui paramétrise les représentations n-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 MRep A n (k) satisfaisant Ext A 2 (M,M)=0 sont réguliers. Ceci généralise aux algèbres engendrées par un nombre fini d’éléments des résultats connus sur les algèbres de dimension finie.

Received : 2014-08-01
Revised : 2015-04-09
Accepted : 2015-09-10
Published online : 2016-12-14
DOI : https://doi.org/10.5802/aif.3037
Classification:  14B05,  16E65,  16S38
Keywords: Noncommutative Geometry, Hochschild Cohomology, Representation Theory
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {3},
     year = {2016},
     pages = {1261-1277},
     doi = {10.5802/aif.3037},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 66 (2016) no. 3, pp. 1261-1277. doi : 10.5802/aif.3037. http://www.numdam.org/item/AIF_2016__66_3_1261_0/

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