A new family of algebras whose representation schemes are smooth
[Une nouvelle famille d’algèbres dont les schémas de représentations sont lisses]
Annales de l'Institut Fourier, Tome 66 (2016) no. 3, pp. 1261-1277.

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.

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.

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DOI : 10.5802/aif.3037
Classification : 14B05, 16E65, 16S38
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

1 Università di Torino Dipartimento di Matematica Via Carlo Alberto n.10 Torino, I-10123 (Italy)
2 Politecnico di Torino Dipartimento di Scienze Matematiche C.so Duca degli Abruzzi n.24 Torino, I-10129 (Italy)
3 ISI Foundation Via Alassio 11/c Torino I-10126 Torino (Italy)
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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. http://www.numdam.org/articles/10.5802/aif.3037/

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