Upper triangular matrices and operations in odd primary connective K-theory

Details Upper triangular matrices and operations in odd primary connective K-theory Upper triangular matrices and operations in odd primary connective K-theory

2012-04-18

arxiv.org/abs/1204.4033v1

Mathematics

Algebraic Topology

26 pages

Scientific paper

We prove analogues for odd primes of results of Snaith and Barker-Snaith. Let l denote the p-complete connective Adams summand and consider the group of left l-module automorphisms of l smash l in the stable homotopy category which induce the identity on mod p homology. We prove a group isomorphism between this group and a certain group of infinite invertible upper triangular matrices with entries in the p-adic integers. We determine information about the matrix corresponding to the automorphism 1 smash Psi^q, where Psi^q is the Adams operation and q is an integer which generates the p-adic units.

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