On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions.

Intro -- 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 k(S[sub(n)])-Submodules of Lie(n) -- 8. The Functor A[sup(min)] over a Field of Characteristic p &gt -- 0 -- 8.1. An upper bound on the size of A[sup(min)](V) -- 8.2. Some general theorems on natural coalgebra retracts of T(V) -- 8.3. A coalgebra filtration on the functor A[sup(min)] -- 8.4. A lower bound on the growth of A[sup(min)](V) -- 9. Proof of Theorems 1.1 and 1.6 -- 10. The Functor L'[sub(n)] and the Associated k(Σ[sub(n)])-Module Lie'(n) -- 11. Examples -- 11.1. The functor A[sup(min)][sub(n)] for n ≤ p -- 11.2. The functor B[sup(max)] -- 11.3. The symmetric group module Lie[sup(max)](p) -- 11.4. Calculations for small n when p = 2 -- 11.5. Decompositions of ΩΣ[sup(2)]X for two-cell complexes X -- 11.6. The PBW map in characteristic 0 -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.