Abstract
An analog of the Freudenthal–Weil theorem holds for the discontinuous homomorphisms of a connected pro-Lie group into a compact group if and only if the radical of the pro-Lie group is amenable.
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References
A. Weil, L’intégration dans les groupes topologiques et ses applications (Hermann & Cie, Paris, 1940).
A. I. Shtern, “Freudenthal–Weil Theorem for Arbitrary Embeddings of Connected Lie Groups in Compact Groups,” Adv. Stud. Contemp. Math. (Kyungshang) 19 (2), 157–164 (2009).
A. I. Shtern, “Connected Lie Groups Having Faithful Locally Bounded (Not Necessarily Continuous) Finite-Dimensional Representations,” Russ. J. Math. Phys. 16 (4), 566–567 (2009).
A. I. Shtern, “A Freudenthal–Weil Theorem for Pro-Lie Groups,” Russ. J. Math. Phys. 22 (4), 546–549 (2015).
K. H. Hofmann and S. A. Morris, The Lie Theory of Connected Pro-Lie Groups. A Structure Theory for Pro-Lie Algebras, Pro-Lie Groups, and Connected Locally Compact Groups (European Mathematical Society, Zürich, 2007).
J. Tits, “Free Subgroups in Linear Groups,” J. Algebra 20, 250–270 (1972).
A. I. Shtern, “Exponential Stability of Quasihomomorphisms into Banach Algebras and a Ger–?Semrl Theorem,” Russ. J. Math. Phys. 22 (1), 135–138 (2015).
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Shtern, A.I. Freudenthal–Weil theorem for pro-Lie groups. Russ. J. Math. Phys. 23, 115–117 (2016). https://doi.org/10.1134/S106192081601009X
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DOI: https://doi.org/10.1134/S106192081601009X