We study p-localizations, where p is an odd prime, of the full subcategories \( {\mathcal{S}}^n \) of stable homotopy category formed by CW-complexes with cells in n successive dimensions. Using the technique of triangulated categories and matrix problems, we classify the atoms (indecomposable objects) in \( {\mathcal{S}}_p^n \) for n ≤ 4(p − 1) and show that, for n > 4(p − 1), this classification is wild in a sense of the representation theory.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 4, pp. 458–472, April, 2014.
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Drozd, Y.A., Kolesnyk, P.O. Atoms in the p-localization of Stable Homotopy Category. Ukr Math J 66, 514–529 (2014). https://doi.org/10.1007/s11253-014-0949-0
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DOI: https://doi.org/10.1007/s11253-014-0949-0