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On natural coalgebra decompositions of tensor algebras and loop suspensions

About this Title

Paul Selick and Jie Wu

Publication: Memoirs of the American Mathematical Society
Publication Year 2000: Volume 148, Number 701
ISBNs: 978-0-8218-2110-7 (print); 978-1-4704-0292-1 (online)
MathSciNet review: 1706247
MSC: Primary 55P35; Secondary 16W30, 16W70

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Table of Contents


  • 1. Introduction
  • 2. Natural coalgebra transformations of tensor algebras
  • 3. Geometric realizations and the proof of Theorem 1.3
  • 4. Existence of minimal natural coalgebra retracts of tensor algebras
  • 5. Some lemmas on coalgebras
  • 6. Functorial version of the Poincaré-Birkhoff-Witt theorem
  • 7. Projective $\mathbf {k}(S_n)$-submodules of $\operatorname {Lie}(n)$
  • 8. The functor $A^{\mathrm {min}}$ over a field of characteristic $p > 0$
  • 9. Proof of Theorems 1.1 and 1.6
  • 10. The functor $L’_n$ and the associated $\mathbf {k}(\Sigma _n)$-module $\operatorname {Lie}’(n)$
  • 11. Examples