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.

DOI:
https://doi.org/10.1090/S0002-9947-01-02705-2

Published electronically:
May 22, 2001

MathSciNet review:
1852092

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Abstract | References | Similar Articles | Additional Information

Let the mod 2 Steenrod algebra, , and the general linear group, , act on with 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 is -decomposable in for arbitrary . 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 are the elements of Hopf invariant one and those of Kervaire invariant one.

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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:
https://doi.org/10.1090/S0002-9947-01-02705-2

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