Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 149, Issue 9, Pages 3991-3997Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/15549
Keywords
Isometry group; pseudo-Riemannian metric; compact Lie group; identity component
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Funding
- National Natural Science Foundation of China [11571182, 11931009]
- Natural Science Foundation of Tianjin [19JCYBJC30600]
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This paper discusses the properties of the isometry group of a simple Lie group G with a left-invariant pseudo-Riemannan metric, proving that the isometry group is compact. It also states that the identity component of the isometry group is compact when G is not simply-connected.
Let G be a connected, simply-connected, compact simple Lie group. In this paper, we show that the isometry group of G with a left-invariant pseudo-Riemannan metric is compact. Furthermore, the identity component of the isometry group is compact if G is not simply-connected.
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