Invariant Theory and the Lambda Algebra

DOI10.2307/1999640zbMath0533.55013OpenAlexW4245167176MaRDI QIDQ3316218

William M. Singer

Publication date: 1983

Full work available at URL: https://doi.org/10.2307/1999640

zbMATH Keywords

invariant theorycoalgebra structureAdams spectral sequence for spheresAdem relationsdual of the lambda algebrahomology of the Steenrod algebralinear group over \({\mathbb{Z}} mod 2\)

Mathematics Subject Classification ID

Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) (18G15) Steenrod algebra (55S10) Adams spectral sequences (55T15) Chain complexes (category-theoretic aspects), dg categories (18G35) Chain complexes in algebraic topology (55U15) (K)-theory operations and generalized cohomology operations in algebraic topology (55S25)

Related Items (22)

Formal partial derivatives and the commutativity of squaring operations ⋮ Sur les foncteurs dérivés de la déstabilisation ⋮ On Singer's invariant-theoretic description of the lambda algebra: A mod \(p\) analogue ⋮ The cohomology of the Steenrod algebra and the mod \(p\) Lannes-Zarati homomorphism ⋮ On unstable modules over the Dickson algebras, the Singer functors \(R_{s}\) and the functors \(Fix_{S}\) ⋮ Lambda algebra and the Singer transfer ⋮ An invariant theoretical description of \(\Lambda \otimes A_*\) ⋮ On the vanishing of the Lannes-Zarati homomorphism ⋮ A representation of the dual of the Steenrod algebra ⋮ The squaring operation on -generators of the Dickson algebra. ⋮ The algebraic transfer for the real projective space ⋮ Algebraic transfer and action of linear groups on mod 2 divided powers ⋮ Spherical classes and the Lambda algebra ⋮ Module structures and the derived functors of iterated loop functors on unstable modules over the Steenrod algebra ⋮ A Phenomenon of Reciprocity in the Universal Steenrod Algebra ⋮ The Iterated Total Squaring Operation ⋮ On the derived functors of destabilization at odd primes ⋮ The transfer in homological algebra ⋮ The generalized algebraic conjecture on spherical classes ⋮ The Lannes-Zarati homomorphism and decomposable elements ⋮ On the mod \(p\) Lannes-Zarati homomorphism ⋮ The Singer transfer for infinite real projective space

Cites Work

• Unnamed Item
• On the action of the Dyer-Lashof algebra in \(H*(G)\)
• The construction of certain algebras over the Steenrod algebra
• Classifying spaces, Steenrod operations and algebraic closure
• Iterated loop functors and the homology of the Steenrod algebra. II. A chain complex for Omega(s,k)M
• The mod-\(p\) lower central series and the Adams spectral sequence
• On the structure of Hopf algebras
• A new chain complex for the homology of the Steenrod algebra
• On a Cartan Formula for Secondary Cohomology Operations.
• A Spectral Sequence for the Homotopy of Nice Spaces

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