Open Access
June 2009 The squaring operation on ${\cal A}$-generators of the Dickson algebra
Nguyên H. V. Hưng, Võ T. N. Quỳnh
Proc. Japan Acad. Ser. A Math. Sci. 85(6): 67-70 (June 2009). DOI: 10.3792/pjaa.85.67


We study the squaring operation $Sq^0$ on the dual of the minimal ${\cal A}$-generators of the Dickson algebra. We show that this squaring operation is isomorphic on its image. We also give vanishing results for this operation in some cases. As a consequence, we prove that the Lannes-Zarati homomorphism vanishes (1) on every element in any finite $Sq^0$-family in $Ext_{\cal A}^*({\bf F}_2, {\bf F}_2)$ except possibly the family initial element, and (2) on almost all known elements in the Ext group. This verifies a part of the algebraic version of the classical conjecture on spherical classes.


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Nguyên H. V. Hưng. Võ T. N. Quỳnh. "The squaring operation on ${\cal A}$-generators of the Dickson algebra." Proc. Japan Acad. Ser. A Math. Sci. 85 (6) 67 - 70, June 2009.


Published: June 2009
First available in Project Euclid: 3 June 2009

zbMATH: 1175.55008
MathSciNet: MR2532421
Digital Object Identifier: 10.3792/pjaa.85.67

Primary: 55P47 , 55Q45 , 55S10 , 55T15

Keywords: cohomology of the Steenrod algebra , invariant theory , Lannes-Zarati homomorphism , modular representations , spherical classes

Rights: Copyright © 2009 The Japan Academy

Vol.85 • No. 6 • June 2009
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