The squaring operation on A{script}-generators of the Dickson algebra

Abstract

We study the squaring operation Sq0 on the dual of the minimal 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 Sq0-family in Ext*A (F2,F2) 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. ©2009 The Japan Academy.