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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 27, Issue 3


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

Laura Stanley / Sarah Whitehouse
Published Online: 2013-03-27 | DOI: https://doi.org/10.1515/forum-2012-0086


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

Keywords: K-theory; cohomology operation; upper triangular matrix

MSC: 55S25; 19L64; 11B65

About the article

Received: 2012-06-21

Revised: 2013-01-04

Published Online: 2013-03-27

Published in Print: 2015-05-01

Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1345–1378, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0086.

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