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The squaring operation on -generators of the Dickson algebra†.

Published online by Cambridge University Press:  03 December 2009

NGUYỄN H. V. HƯNG  and
VÕ T. N. QUỲNH
NGUYỄN H. V. HƯNG
Affiliation:
Department of Mathematics, Vietnam National University, Hanoi 334 Nguyễn Trãi Street, Hanoi, Vietnam e-mail: nhvhung@vnu.edu.vn e-mail: quynhvtn@vnu.edu.vn
VÕ T. N. QUỲNH
Affiliation:
Department of Mathematics, Vietnam National University, Hanoi 334 Nguyễn Trãi Street, Hanoi, Vietnam e-mail: nhvhung@vnu.edu.vn e-mail: quynhvtn@vnu.edu.vn
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Abstract

We study the squaring operation Sq0 on the dual of the minimal -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 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 2 , March 2010 , pp. 267 - 288
Copyright
Copyright © Cambridge Philosophical Society 2009

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