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Connected Lie Groups that Act Freely on a Product of Linear Spheres
Author(s) -
Greenlees J. P. C.,
Pérez J. A.
Publication year - 1996
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/28.6.634
Subject(s) - mathematics , lie group , spheres , abelian group , product (mathematics) , action (physics) , pure mathematics , combinatorics , geometry , physics , quantum mechanics , astronomy
In this note we prove that a compact connected Lie group G admits a free action on some product of linear spheres if and only if it is isomorphic to (T k × SU(2) l )/ Z for some k and l and for some central elementary abelian 2‐subgroup Z with Z ∩ SU(2)M l = 1.
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