AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

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: https://doi.org/10.1090/memo/0701
MathSciNet review: 1706247
MSC: Primary 55P35; Secondary 16W30, 16W70

View full volume as PDF

Read more about this volume

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