Exotic groups and quotients of loop groups
Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1313-1323 Cet article a éte moissonné depuis la source Math-Net.Ru

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A study is made of various category-theoretic properties of exotic groups. Exotic groups that are non-commutative and non-metrizable are constructed for the first time. A proof is given of a theorem on the construction of exotic groups by means of groups of continuous maps (or maps of smoothness $r<\infty$) from a real complete space (respectively, a locally compact manifold) to a locally compact group (respectively, a Lie group) via factorization. It is shown that quotients of loop groups or generalized loop groups with respect to their closed normal subgroups are either commutative exotic groups, or else non-exotic groups.
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S. V. Lyudkovskii. Exotic groups and quotients of loop groups. Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1313-1323. http://geodesic.mathdoc.fr/item/SM_1995_186_9_a4/

[1] Herer W., Christensen J., “On the existence of pathological submeasures and the construction of exotic topological groups”, Math. Annal., 213:3 (1975), 203–210 | DOI | MR | Zbl

[2] Banaszczyk W., “On the existence of exotic Banach–Lie groups”, Math. Annal., 264:4 (1983), 485–493 | DOI | MR | Zbl

[3] Banaszczyk W., Additive subgroups of topological vector spaces, Springer-Verlag, Berlin, 1991 | MR

[4] Danford N., Schvarts Dzh., Lineinye operatory, 1962; ИЛ, М., 1966

[5] Naimark M. A., Normirovannye koltsa, Nauka, M., 1968 | MR | Zbl

[6] Engelking R., Obschaya topologiya, Mir, M., 1986 | MR

[7] Khyuitt E., Ross K., Abstraktnyi garmonicheskii analiz, Nauka, M., 1975

[8] Shefer Kh., Topologicheskie vektornye prostranstva, Mir, M., 1971 | MR

[9] Narici L., Beckenstein E., Topological vector spaces, MD, New York, 1985 | MR

[10] Pich A., Yadernye lokalno vypuklye prostranstva, Mir, M., 1967 | MR

[11] Pressli E., Sigal G., Gruppy petel, Mir, M., 1990 | MR

[12] Pontryagin L. S., Nepreryvnye gruppy, Nauka, M., 1984 | MR

[13] Montgomery D., Zippin L., Topological transformation groups, J. Wiley Sons, New York, 1955 | MR

[14] Burbaki N., Gruppy i algebry Li, Mir, M., 1976 | MR

[15] Ruiz L. M. S., Pellicer M. L., “On linearly topologized spaces and real-compact spaces, II”, Portugal. Math., 48:4 (1991), 475–482 | MR | Zbl

[16] Markov A. A., “O svobodnykh topologicheskikh gruppakh”, Izv. AN SSSR. Ser. matem., 9:1 (1945), 3–64 | MR

[17] Mitchell B., Theory of categories, Acad. Press, New York, 1965 | MR | Zbl