Transfert algébrique et action du groupe linéaire sur les puissances divisées modulo 2  [ Algebraic transfer and action of linear groups on mod 2 divided powers ]
Annales de l'Institut Fourier, Volume 58 (2008) no. 5, p. 1785-1837

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.

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.

DOI : https://doi.org/10.5802/aif.2399
Classification:  55S10
Keywords: Steenrod algebra, linear groups, divided powers
@article{AIF_2008__58_5_1785_0,
     author = {Nam, Tran Ngoc},
     title = {Transfert alg\'ebrique et action du groupe lin\'eaire sur les puissances divis\'ees modulo~2},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {5},
     year = {2008},
     pages = {1785-1837},
     doi = {10.5802/aif.2399},
     mrnumber = {2445834},
     zbl = {1152.55010},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2008__58_5_1785_0}
}
Nam, Tran Ngoc. Transfert algébrique et action du groupe linéaire sur les puissances divisées modulo 2. Annales de l'Institut Fourier, Volume 58 (2008) no. 5, pp. 1785-1837. doi : 10.5802/aif.2399. http://www.numdam.org/item/AIF_2008__58_5_1785_0/

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