Higher homotopy associativity in the Harris decomposition of Lie groups

Daisuke Kishimoto; Toshiyuki Miyauchi

doi:10.1017/prm.2019.57

Higher homotopy associativity in the Harris decomposition of Lie groups

Daisuke Kishimoto, Toshiyuki Miyauchi

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2982-3000
Number of pages	19
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	150
Issue number	6
DOIs	https://doi.org/10.1017/prm.2019.57
Publication status	Published - Dec 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1017/prm.2019.57

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title = "Higher homotopy associativity in the Harris decomposition of Lie groups",

abstract = "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.",

author = "Daisuke Kishimoto and Toshiyuki Miyauchi",

note = "Funding Information: We are grateful to Mitsunobu Tsutaya for useful advices on An-structures and to the referee for pointing out an ambiguity in the calculation of a Samelson product in Spin(8) in the earlier version and for the suggestion to add theorem 1.4. The first author was supported in part by JSPS KAKENHI (No. 17K05248). Publisher Copyright: Copyright {\textcopyright} 2019 The Royal Society of Edinburgh.",

year = "2020",

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doi = "10.1017/prm.2019.57",

language = "English",

volume = "150",

pages = "2982--3000",

journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",

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AU - Miyauchi, Toshiyuki

N1 - Funding Information: We are grateful to Mitsunobu Tsutaya for useful advices on An-structures and to the referee for pointing out an ambiguity in the calculation of a Samelson product in Spin(8) in the earlier version and for the suggestion to add theorem 1.4. The first author was supported in part by JSPS KAKENHI (No. 17K05248). Publisher Copyright: Copyright © 2019 The Royal Society of Edinburgh.

PY - 2020/12

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N2 - 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.

AB - 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.

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JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

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ER -

Higher homotopy associativity in the Harris decomposition of Lie groups

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