The homomorphisms between the Dickson–Mùi algebras as modules over the Steenrod algebra

Nguyễn H.V. Hưng

doi:10.1016/j.crma.2010.07.032

Topology

The homomorphisms between the Dickson–Mùi algebras as modules over the Steenrod algebra

Christophe Soulé

Nguyễn H.V. Hưng ¹

¹Department of Mathematics, Vietnam National University, Hanoi, 334 Nguyễn Trãi Street, Hanoi, Viet Nam

Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 1001-1004

Abstract (Original language)
Résumé

The Dickson–Mùi algebra consists of all invariants in the mod p cohomology of an elementary abelian p-group under the general linear group. It is a module over the Steenrod algebra, $A$ . We determine explicitly all the $A$ -module homomorphisms between the Dickson–Mùi algebras and all the $A$ -module automorphisms of these algebras.

L'algèbre de Dickson–Mùi consiste en les invariants sous l'action du groupe linéaire dans l'algèbre de cohomologie modulo p d'un p-groupe abélien élémentaire. C'est un module sur l'algèbre de Steenrod $A$ . Nous déterminons explicitement tous les homorphismes $A$ -linéaires entre ces algèbres ainsi que leurs automorphismes ( $A$ -linéaires).

Article information
Cite this article

Received: 2010-04-27
Accepted: 2010-07-30
Published online: 2010-09-01

DOI: 10.1016/j.crma.2010.07.032

Author's affiliations:

Nguyễn H.V. Hưng ¹

¹ Department of Mathematics, Vietnam National University, Hanoi, 334 Nguyễn Trãi Street, Hanoi, Viet Nam

Nguyễn H.V. Hưng. The homomorphisms between the Dickson–Mùi algebras as modules over the Steenrod algebra. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 1001-1004. doi: 10.1016/j.crma.2010.07.032

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^☆ The work was supported in part by a grant of the NAFOSTED.

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