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

Laura Stanley; Sarah Whitehouse

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arXiv · 1204.4033

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

Laura Stanley·Sarah Whitehouse

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Abstract

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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Laura Stanley, Sarah Whitehouse. 2012-04-18. Upper triangular matrices and operations in odd primary connective K-theory. https://arxiv.org/abs/1204.4033

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