# 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)

DOI: http://dx.doi.org/10.1090/memo/0701

MathSciNet review: 1706247

MSC: Primary 55P35; Secondary 16W30, 16W70

### Table of Contents

**Chapters**

- 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