Graded morphisms of G-modules
Annales de l'Institut Fourier, Volume 37 (1987) no. 4, pp. 161-166.

Let A be finite dimensional C-algebra which is a complete intersection, i.e. A=C[X 1 ,...,X n ]/(f 1 ,...,f n ) whith a regular sequences f 1 ,...,f n . Steve Halperin conjectured that the connected component of the automorphism group of such an algebra A is solvable. We prove this in case A is in addition graded and generated by elements of degree 1.

Soit A une algèbre sur C de dimension finie, qui est une instersection complète, c’est-à-dire A=C[X 1 ,...,X n ]/(f 1 ,...,f n ) pour une suite régulière f 1 ,...,f n . Steve Halperin a conjecturé que dans ce cas la composante connexe du groupe d’automorphisme de A est résoluble. On démontre cette conjecture lorsque l’algèbre A est graduée et engendrée par des éléments de degré un.

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     title = {Graded morphisms of $G$-modules},
     journal = {Annales de l'Institut Fourier},
     pages = {161--166},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {37},
     number = {4},
     year = {1987},
     doi = {10.5802/aif.1115},
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Kraft, Hanspeter; Procesi, Claudio. Graded morphisms of $G$-modules. Annales de l'Institut Fourier, Volume 37 (1987) no. 4, pp. 161-166. doi : 10.5802/aif.1115. http://archive.numdam.org/articles/10.5802/aif.1115/

[1] H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspekte der Mathematik D1, Vieweg-Verlag, 1985. | Zbl

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