Noncommutativity of the group of self homotopy classes of Lie groups

DOI10.1016/S0166-8641(01)00261-9zbMath1012.55019WikidataQ115339623 ScholiaQ115339623MaRDI QIDQ1862075

Martin Arkowitz, Hideaki Ōshima, Jeffrey A. Strom

Publication date: 10 March 2003

Published in: Topology and its Applications (Search for Journal in Brave)

zbMATH Keywords

Lie groupnilpotency classself homotopy class

Mathematics Subject Classification ID

Homotopy groups, general; sets of homotopy classes (55Q05) Homotopy groups of topological groups and homogeneous spaces (57T20)

Related Items (8)

On a conjecture of Ōshima ⋮ A note on the Samelson products in \(\pi_*(SO(2n))\) and the group \([SO(2n),SO(2n)\)] ⋮ On Samelson products in \(p\)-localized unitary groups ⋮ On localized self-homotopy groups of \(SU(4)\) and \(Sp(4)\) ⋮ Homotopy groups of the spaces of self-maps of Lie groups ⋮ Commutativity of localized self-homotopy groups of symplectic groups ⋮ On the commutativity of the localized self homotopy groups of \(SU(n)\) ⋮ Self homotopy groups with large nilpotency classes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
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• A note on the Samelson product in the classical groups
• On the Lusternik-Schnirelmann category of Lie groups
• Self homotopy groups of Hopf spaces with at most three cells
• Self homotopy group of the exceptional Lie group \(G_2\)
• Nilpotence and finite H-spaces
• \(Spin\;(n)\) is not homotopy nilpotent for \(n{\geq}7\)
• Homotopy commutative H-spaces
• The embeddings \(O(n)\subset U(n)\) and \(U(n)\subset Sp(n)\), and a Samelson product
• On homotopy commutative H-spaces
• Cohomology operations and the homotopy of compact Lie groups. I
• On the homotopy groups of the classical groups
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• Groupes d'homotopie et classes de groupes abéliens
• On mappings into group-like spaces
• Multiplication on Spheres (II)
• ON H-SPACES AND THEIR HOMOTOPY GROUPS
• The self homotopy set of a Hopf-space
• Products on spheres
• Groupes de Lie et Puissances Reduites de Steenrod
• On homotopy-commutativity
• On homotopy-commutativity
• Homotopy classes that are trivial mod \({\mathcal F}\)
• Non commutativity of self homotopy groups

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