A new action of the Kudo-Araki-May algebra on the dual of the symmetric algebras, with applications to the hit problem

DOI10.2140/agt.2011.11.1767zbMath1220.55009OpenAlexW2081721793MaRDI QIDQ541309

Frank Williams, David J. Pengelley

Publication date: 7 June 2011

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/agt.2011.11.1767

zbMATH Keywords

Steenrod algebrasymmetric algebrahit problemBOBUDyer-Lashof algebraKudo-Araki-May algebra

Mathematics Subject Classification ID

Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Homology and cohomology of Lie groups (57T10) Graded rings and modules (associative rings and algebras) (16W50) Steenrod algebra (55S10) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Dyer-Lashof operations (55S12) Homology and homotopy of (Bmathrm{O}) and (Bmathrm{U}); Bott periodicity (55R45) Hopf algebras (aspects of homology and homotopy of topological groups) (57T05) Bialgebras (16T10) Homology and cohomology of (H)-spaces (57T25) Hopf algebras and their applications (16T05)

Related Items

On Peterson's open problem and representations of the general linear groups ⋮ On the dimension of \(H^\ast( ( \mathbb{Z}_2 )^{\times t}, \mathbb{Z}_2)\) as a module over Steenrod ring ⋮ Sparseness for the symmetric hit problem at all primes ⋮ The hit problem for \(H^{*}(BU(2); \mathbb F_p)\) ⋮ The Dyer-Lashof algebra and the hit problems

Cites Work

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• Embedding the flag representation in divided powers
• The transfer in homological algebra
• Generators of the cohomology of \(BV_3\)
• Generic \(\mathcal A\)-generators for the polynomial algebra
• The hit problem for \(H^{*}(BU(2); \mathbb F_p)\)
• Rings of symmetric functions as modules over the Steenrod algebra
• Steenrod squares of polynomials and the Peterson conjecture
• A-generators for certain polynomial algebras
• Homology of the classical groups over the Dyer-Lashof algebra
• Generating H*(BO(3), ${\bb F}_2$) as a module over the Steenrod algebra
• The hit problem for symmetric polynomials over the Steenrod algebra
• On the behavior of the algebraic transfer
• Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology
• Sub-Hopf algebras of the Steenrod algebra and the Singer transfer
• The odd-primary Kudo-Araki-May algebra of algebraic Steenrod operations and invariant theory
• The cohomology of the Steenrod algebra and representations of the general linear groups