Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The hit problem for the Dickson algebra


Authors: Nguyen H. V. Hu'ng and Tran Ngoc Nam
Journal: Trans. Amer. Math. Soc. 353 (2001), 5029-5040
MSC (2000): Primary 55S10; Secondary 55P47, 55Q45, 55T15.
Published electronically: May 22, 2001
MathSciNet review: 1852092
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

Let the mod 2 Steenrod algebra, $\mathcal{A}$, and the general linear group, $GL(k,{\mathbb{F} }_2)$, act on $P_{k}:={\mathbb{F} }_2[x_{1},...,x_{k}]$ with $\vert x_{i}\vert=1$ in the usual manner. We prove the conjecture of the first-named author in Spherical classes and the algebraic transfer, (Trans. Amer. Math Soc. 349 (1997), 3893-3910) stating that every element of positive degree in the Dickson algebra $D_{k}:=(P_{k})^{GL(k, {\mathbb{F} }_2)}$ is $\mathcal{A}$-decomposable in $P_{k}$ for arbitrary $k>2$. This conjecture was shown to be equivalent to a weak algebraic version of the classical conjecture on spherical classes, which states that the only spherical classes in $Q_0S^0$ are the elements of Hopf invariant one and those of Kervaire invariant one.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 55S10, 55P47, 55Q45, 55T15.

Retrieve articles in all journals with MSC (2000): 55S10, 55P47, 55Q45, 55T15.


Additional Information

Nguyen H. V. Hu'ng
Affiliation: Department of Mathematics, Vietnam National University, Hanoi, 334 Nguyên Trãi Street, Hanoi, Vietnam
Email: nhvhung@hotmail.com

Tran Ngoc Nam
Affiliation: Department of Mathematics, Vietnam National University, Hanoi, 334 Nguyên Trãi Street, Hanoi, Vietnam
Email: trngnam@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02705-2
PII: S 0002-9947(01)02705-2
Keywords: Steenrod algebra, invariant theory, Dickson algebra.
Received by editor(s): September 29, 1999
Received by editor(s) in revised form: February 22, 2000
Published electronically: May 22, 2001
Additional Notes: This work was supported in part by the National Research Project, No. 1.4.2
Dedicated: Dedicated to Professor Franklin P. Peterson on the occasion of his 70th birthday
Article copyright: © Copyright 2001 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia