Abstract
We construct a Polish group with an invariant metric in which Lie sums and Lie brackets do not exist. The construction of the group and the proof of the main theorem use some facts of combinatorial nature about the free group with two generators equipped with a Graev metric.
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Ding, L., Gao, S.: Graev metric groups and Polishable subgroups. Adv. Math 213, 887–901 (2007)
Graev, M.I.: Free topological groups. Am. Math. Soc. Transl. 35, 61 (1951)
Montgomery, D., Zippin, L.: Topological Transformation Groups. Interscience, New York (1955)
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Communicated by B. Löwe.
The second author acknowledges the United States NSF grant DMS-0501039 for the support of his research.
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van den Dries, L., Gao, S. A Polish group without Lie sums. Abh. Math. Semin. Univ. Hambg. 79, 135–147 (2009). https://doi.org/10.1007/s12188-009-0019-y
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DOI: https://doi.org/10.1007/s12188-009-0019-y