Comptes Rendus
no. 11-12
Algebra/Topology
Division of the Dickson algebra by the Steinberg unstable module
[Division de lʼalgèbre de Dickson par le module instable de Steinberg]

Présenté par : the Editorial Board

Nguyen Dang Ho Hai1
1 University of Hue, College of Sciences, 77 Nguyen Hue Street, Hue City, Viet Nam
Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 425-428.

On détermine la division de lʼalgèbre de Dickson par le module instable de Steinberg dans la catégorie des modules instables sur lʼalgèbre de Steenrod modulo 2.

We compute the division of the Dickson algebra by the Steinberg unstable module in the category of unstable modules over the mod-2 Steenrod algebra.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.07.010
Nguyen Dang Ho Hai 1

1 University of Hue, College of Sciences, 77 Nguyen Hue Street, Hue City, Viet Nam 
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Nguyen Dang Ho Hai. Division of the Dickson algebra by the Steinberg unstable module. Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 425-428. doi : 10.1016/j.crma.2013.07.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.07.010/

[1] Leonard Eugene Dickson A fundamental system of invariants of the general modular linear group with a solution of the form problem, Trans. Amer. Math. Soc., Volume 12 (1911) no. 1, pp. 75-98

[2] Nguyen Dang Ho Hai; Lionel Schwartz; Tran Ngoc Nam La fonction génératrice de Minc et une « conjecture de Segal » pour certains spectres de Thom, Adv. Math., Volume 225 (2010) no. 3, pp. 1431-1460

[3] Nicholas J. Kuhn Chevalley group theory and the transfer in the homology of symmetric groups, Topology, Volume 24 (1985) no. 3, pp. 247-264

[4] Nicholas J. Kuhn The rigidity of L(n), Seattle, Wash., 1985 (Lecture Notes in Math.), Volume vol. 1286, Springer, Berlin (1987), pp. 286-292

[5] Jean Lannes Sur les espaces fonctionnels dont la source est le classifiant dʼun p-groupe abélien élémentaire, Inst. Hautes Études Sci. Publ. Math., Volume 75 (1992), pp. 135-244 (With an appendix by Michel Zisman)

[6] Jean Lannes; Saïd Zarati Sur les foncteurs dérivés de la déstabilisation, Math. Z., Volume 194 (1987) no. 1, pp. 25-59

[7] Stephen A. Mitchell; Stewart B. Priddy Stable splittings derived from the Steinberg module, Topology, Volume 22 (1983) no. 3, pp. 285-298

[8] Lionel Schwartz Unstable Modules over the Steenrod Algebra and Sullivanʼs Fixed Point Set Conjecture, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1994

[9] Robert Steinberg Prime power representations of finite linear groups, Canad. J. Math., Volume 8 (1956), pp. 580-591

Cité par Sources :

☆ This note was written while the author was a postdoctoral researcher (4/2011–4/2012) at “Institut de recherche en mathématique et physique” (IRMP) and was revised while the author was a visitor (9/2012) at “Vietnam Institute for Advanced Study in Mathematics” (VIASM). The author would like to thank both institutes for their hospitality.

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