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2011 A new action of the Kudo–Araki–May algebra on the dual of the symmetric algebras, with applications to the hit problem
David Pengelley, Frank Williams
Algebr. Geom. Topol. 11(3): 1767-1780 (2011). DOI: 10.2140/agt.2011.11.1767

Abstract

The hit problem for a cohomology module over the Steenrod algebra A asks for a minimal set of A–generators for the module. In this paper we consider the symmetric algebras over the field Fp, for p an arbitrary prime, and treat the equivalent problem of determining the set of A–primitive elements in their duals. We produce a method for generating new primitives from known ones via a new action of the Kudo–Araki–May algebra K, and consider the K–module structure of the primitives, which form a sub K–algebra of the dual of the infinite symmetric algebra. Our examples show that the K–action on the primitives is not free. Our new action encompasses, on the finite symmetric algebras, the operators introduced by Kameko for studying the hit problem.

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David Pengelley. Frank Williams. "A new action of the Kudo–Araki–May algebra on the dual of the symmetric algebras, with applications to the hit problem." Algebr. Geom. Topol. 11 (3) 1767 - 1780, 2011. https://doi.org/10.2140/agt.2011.11.1767

Information

Received: 10 July 2010; Revised: 9 February 2011; Accepted: 6 March 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1220.55009
MathSciNet: MR2821440
Digital Object Identifier: 10.2140/agt.2011.11.1767

Subjects:
Primary: 16T05, 16T10, 16W22, 55R45, 55S10, 55S12
Secondary: 16W50, 55R40, 57T05, 57T10, 57T25

Rights: Copyright © 2011 Mathematical Sciences Publishers

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