TY  - BOOK
AU  - Selick,Paul
AU  - Wu,Jie
TI  - On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions
T2  - Memoirs of the American Mathematical Society
SN  - 9781470402921
AV  - QA612.76 -- .S45 2000eb 
U1  - 510 s;514/.24 
PY  - 2000///
CY  - Providence
PB  - American Mathematical Society
KW  - Loop spaces
KW  - H-spaces
KW  - Representations of groups
KW  - Electronic books
N1  - 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114446
ER  -