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On invariant operations on pseudo-Riemannian manifolds

Jan Slovák (1992)

Commentationes Mathematicae Universitatis Carolinae

Invariant polynomial operators on Riemannian manifolds are well understood and the knowledge of full lists of them becomes an effective tool in Riemannian geometry, [Atiyah, Bott, Patodi, 73] is a very good example. The present short paper is in fact a continuation of [Slovák, 92] where the classification problem is reconsidered under very mild assumptions and still complete classification results are derived even in some non-linear situations. Therefore, we neither repeat the detailed exposition...

On irreducible, infinite, nonaffine Coxeter groups

Dongwen Qi (2007)

Fundamenta Mathematicae

The following results are proved: The center of any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group is trivial; Any finite index subgroup of an irreducible, infinite, nonaffine Coxeter group cannot be expressed as a product of two nontrivial subgroups. These two theorems imply a unique decomposition theorem for a class of Coxeter groups. We also prove that the orbit of each element other than the identity under the conjugation action in an irreducible, infinite, nonaffine...

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