AN ALGEBRAIC MODEL FOR CHAINS ON Omega BG(p)(boolean AND)

摘要

We provide an interpretation of the homology of the loop space on the p-completion of the classifying space of a finite group in terms of representation theory, and demonstrate how to compute it. We then give the following reformulation. If f is an idempotent in kG such that f.kG is the projective cover of the trivial module k, and e = 1 - f, then we exhibit isomorphisms for n >= 2: H-n(Omega BG(p)(<^>); k) congruent to Tor(n-1)(e.kG.e) (kG.e, e.kG), H-n(Omega BG(p)(<^>); k) congruent to Ext(e.kG.e)(n-1) (e.KG, e.kG). Further algebraic structure is examined, such as products and coproducts, restriction and Steenrod operations.