For certain pairs of Lie groups (G, H) and primes p, Harris showed a relation of the p-localized homotopy groups of G and H. This is reinterpreted as a p-local homotopy equivalence G ≃ (p)H × G/H, and so there is a projection G(p) → H(p). We show how much this projection preserves the higher homotopy associativity.

中文翻译：

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李群的哈里斯分解中更高的同伦结合性

对于某些李群对 (G,H) 和素数p, 哈里斯展示了一个关系p-局部同伦群G和H. 这被重新解释为p-局部同伦等价G≃(p)H×G/H，所以有一个投影G(p)→H(p). 我们展示了这个投影在多大程度上保留了更高的同伦关联性。