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Journal of Lie Theory 32 (2022), No. 3, 697--708
Copyright Heldermann Verlag 2022

A Characteristic-Index Inequality for Closed Embeddings of Locally Compact Groups

Alexandru Chirvasitu
Dept. of Mathematics, University at Buffalo, New York, U.S.A.


The characteristic index of a locally compact connected group $G$ is the non-negative integer $d$ for which we have a homeomorphism $G\cong K\times \mathbb{R}^d$ with $K$ maximal compact in $G$. We prove that the characteristic indices of closed connected subgroups are dominated by those of the ambient groups.

Keywords: Lie group, locally compact group, characteristic index, dense embedding, Lie algebra, homology, fibration, spectral sequence.

MSC: 22D05, 22E15, 22E60, 57T15, 55T10.

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