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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∧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∧Ψ  q   of ℓ∧ℓ, where Ψ  q   is the Adams operation and  q  is an integer which generates the  p -adic units.

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