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The odd-primary Kudo–Araki–May algebra of algebraic Steenrod operations and invariant theory

David J Pengelley and Frank Williams

Geometry & Topology Monographs 11 (2007) 217–243

DOI: 10.2140/gtm.2007.11.217

arXiv: 0903.4988

Abstract

We describe bialgebras of lower-indexed algebraic Steenrod operations over the field with p elements, p an odd prime. These go beyond the operations that can act nontrivially in topology, and their duals are closely related to algebras of polynomial invariants under subgroups of the general linear groups that contain the unipotent upper triangular groups. There are significant differences between these algebras and the analogous one for p=2, in particular in the nature and consequences of the defining Adem relations.

Keywords

algebras of invariants, Kudo–Araki–May algebra, Steenrod algebra, Dyer–Lashof algebra, bialgebras, Nishida relations, Adem relations

Mathematical Subject Classification

Primary: 16W22

Secondary: 16W30, 16W50, 55S10, 55S12, 55S99, 57T05

References
Publication

Received: 1 March 2005
Revised: 24 January 2006
Accepted: 2 February 2006
Published: 14 November 2007

Authors
David J Pengelley
New Mexico State University
Las Cruces NM 88003
USA
Frank Williams
New Mexico State University
Las Cruces NM 88003
USA