Transfert algébrique et action du groupe linéaire sur les puissances divisées modulo 2

Nam, Tran Ngoc

Annales de l'Institut Fourier, Tome 58 (2008) no. 5, pp. 1785-1837.

On détermine la dimension d’une représentation du groupe linéaire définie par un sous-espace vectoriel de l’algèbre à puissances divisées, puis on explicite l’image du transfert algébrique en degré générique et celle du transfert algébrique quadruple, et finalement on identifie les indécomposables de degré pair de l’algèbre polynomiale à quatre variables, vue comme module sur l’algèbre de Steenrod.

We compute the dimension of an algebra with divided powers viewed as a representation of the general linear group, then compute the image of the algebraic transfer in generic degrees, and determine the indecomposable elements of even degree in the polynomial algebra in four variables viewed as a module over the Steenrod algebra.

Classification : 55S10
Mot clés : algèbre de Steenrod, groupe linéaire, puissances divisées
Keywords: Steenrod algebra, linear groups, divided powers

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