Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups
Sbornik. Mathematics, Tome 208 (2017) no. 10, pp. 1557-1576 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe the structure of finite-dimensional locally bounded finally precontinuous quasirepresentations of arbitrary connected locally compact groups. Bibliography: 40 titles.
Keywords: locally compact group, locally bounded map, quasirepresentation, pseudorepresentation, Guichardet-Wigner pseudocharacter.
@article{SM_2017_208_10_a7,
     author = {A. I. Shtern},
     title = {Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups},
     journal = {Sbornik. Mathematics},
     pages = {1557--1576},
     year = {2017},
     volume = {208},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_10_a7/}
}
TY  - JOUR
AU  - A. I. Shtern
TI  - Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups
JO  - Sbornik. Mathematics
PY  - 2017
SP  - 1557
EP  - 1576
VL  - 208
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/SM_2017_208_10_a7/
LA  - en
ID  - SM_2017_208_10_a7
ER  - 
%0 Journal Article
%A A. I. Shtern
%T Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups
%J Sbornik. Mathematics
%D 2017
%P 1557-1576
%V 208
%N 10
%U http://geodesic.mathdoc.fr/item/SM_2017_208_10_a7/
%G en
%F SM_2017_208_10_a7
A. I. Shtern. Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups. Sbornik. Mathematics, Tome 208 (2017) no. 10, pp. 1557-1576. http://geodesic.mathdoc.fr/item/SM_2017_208_10_a7/

[1] R. Dedekind, “Erlauterungen zu den Fragmenten XXVIII”, Collected works of Bernhard Riemann, Dover, New York, 1953, 466–478

[2] H. Rademacher, “Zur Theorie der Modulfunktionen”, J. Reine Angew. Math., 1932:167 (1932), 312–336 | DOI | MR | Zbl

[3] D. H. Hyers, “On the stability of the linear functional equation”, Proc. Nat. Acad. Sci. U. S. A., 27 (1941), 222–224 | DOI | MR | Zbl

[4] D. H. Hyers, S. M. Ulam, “On approximate isometries”, Bull. Amer. Math. Soc., 51 (1945), 288–292 | DOI | MR | Zbl

[5] D. H. Hyers, T. M. Rassias, “Approximate homomorphisms”, Aequationes Math., 44:2-3 (1992), 125–153 | DOI | MR | Zbl

[6] D. Montgomery, L. Zippin, “A theorem on Lie groups”, Bull. Amer. Math. Soc., 48 (1942), 448–452 | DOI | MR | Zbl

[7] J. von Neumann, “Approximative properties of matrices of high finite order”, Portugaliae Math., 3 (1942), 1–62 | MR | MR | Zbl | Zbl

[8] K. Grove, H. Karcher, E. A. Ruh, “Jacobi fields and Finsler metrics on a compact Lie groups with an application to differential pinching problems”, Math. Ann., 211 (1974), 7–21 | DOI | MR | Zbl

[9] J. Baker, J. Lawrence, F. Zorzitto, “The stability of the equation $f(x+y)=f(x)f(y)$”, Proc. Amer. Math. Soc., 74:2 (1979), 242–246 | DOI | MR | Zbl

[10] A. I. Shtern, “On stability of homomorphisms in the group $\mathbb R^*$”, Moscow Univ. Math. Bull., 37:3 (1982), 33–36 | MR | Zbl

[11] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127, Amer. Math. Soc., Providence, RI, 1972, iii+96 pp. | MR | Zbl

[12] A. I. Shtern, “The pseudocharacter determined by the Rademacher symbol”, Russian Math. Surveys, 45:3 (1990), 224–225 | DOI | MR | Zbl

[13] A. I. Shtern, “Quasisymmetry. I”, Russ. J. Math. Phys., 2:3 (1994), 353–382 | MR | Zbl

[14] R. Brooks, “Some remarks on bounded cohomology”, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, NY, 1978), Ann. of Math. Stud., 97, Princeton Univ. Press, Princeton, NJ, 1981, 53–63 | MR | Zbl

[15] A. I. Shtern, “Ustoichivost predstavlenii i psevdokharaktery”, Lomonosovskie chteniya, MGU, M., 1983

[16] V. A. Faiziev, “Pseudocharacters on free products of semigroups”, Funct. Anal. Appl., 21:1 (1987), 77–79 | DOI | MR | Zbl

[17] V. A. Faiziev, “Pseudocharacters on free groups and on certain group constructions”, Russian Math. Surveys, 43:5 (1988), 219–220 | DOI | MR | Zbl

[18] R. I. Grigorchuk, “Some results on bounded cohomology”, Combinatorial and geometric group theory (Edinburgh, 1993), London Math. Soc. Lecture Notes Ser., 204, Cambridge Univ. Press, Cambridge, 1995, 111–163 | MR | Zbl

[19] N. Monod, Continuous bounded cohomology of locally compact groups, Lecture Notes in Math., 1758, Springer-Verlag, Berlin, 2001, x+214 pp. | DOI | MR | Zbl

[20] D. Calegari, scl, MSJ Mem., 20, Math. Soc. Japan, Tokyo, 2009, xii+209 pp. | DOI | MR | Zbl

[21] D. Kotschick, “What is ...a quasi-morphism?”, Notices Amer. Math. Soc., 51:2 (2004), 208–209 | MR | Zbl

[22] A. I. Shtern, “Kazhdan–Mil'man problem for semisimple compact Lie groups”, Russian Math. Surveys, 62:1 (2007), 113–174 | DOI | DOI | MR | Zbl

[23] A. I. Shtern, “Quasirepresentations of amenable groups: results, errors, and hopes”, Russ. J. Math. Phys., 20:2 (2013), 239–253 | DOI | MR | Zbl

[24] R. Ger, P. Šemrl, “The stability of the exponential equation”, Proc. Amer. Math. Soc., 124:3 (1996), 779–787 | DOI | MR | Zbl

[25] A. I. Shtern, “Exponential stability of quasihomomorphisms into Banach algebras and a Ger–Šemrl theorem”, Russ. J. Math. Phys., 22:1 (2015), 141–142 | DOI | MR | Zbl

[26] A. I. Shtern, “Unbounded tame quasirepresentations with commutative discrepancies for amenable groups”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 16:3 (2013), 1350025, 8 pp. | DOI | MR | Zbl

[27] J. Lawrence, “The stability of multiplicative semigroup homomorphisms to real normed algebras. I”, Aequationes Math., 28:1-2 (1985), 94–101 | DOI | MR | Zbl

[28] F. Cabello Sánchez, “Pseudo-characters and almost multiplicative functionals”, J. Math. Anal. Appl., 248:1 (2000), 275–289 | DOI | MR | Zbl

[29] M. Burger, N. Ozawa, A. Thom, “On Ulam stability”, Israel J. Math., 193:1 (2013), 109–129 | DOI | MR | Zbl

[30] C. Moore, A. Russell, “Approximate representations, approximate homomorphisms, and low-dimensional embeddings of groups”, SIAM J. Discrete Math., 29:1 (2015), 182–197 | DOI | MR | Zbl

[31] A. I. Shtern, “Structure properties and real continuous bounded 2-cohomology of locally compact groups”, Funct. Anal. Appl., 35:4 (2001), 294–304 | DOI | DOI | MR | Zbl

[32] A. I. Shtern, “Bounded continuous real $2$-cocycles on simply connected simple Lie groups and their applications”, Russ. J. Math. Phys., 8:1 (2001), 122–133 | MR | Zbl

[33] A. I. Shtern, “A version of van der Waerden's theorem and a proof of Mishchenko's conjecture on homomorphisms of locally compact groups”, Izv. Math., 72:1 (2008), 169–205 | DOI | DOI | MR | Zbl

[34] A. I. Shtern, “Quasisymmetry. II”, Russ. J. Math. Phys., 14:3 (2007), 332–356 | DOI | MR | Zbl

[35] A. I. Shtern, “Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture”, J. Math. Sci. (N. Y.), 159:5 (2009), 653–751 | DOI | MR | Zbl

[36] A. I. Shtern, “The structure of locally bounded finite-dimensional representations of connected locally compact groups”, Sb. Math., 205:4 (2014), 600–611 | DOI | DOI | MR | Zbl

[37] A. I. Shtern, “Corrected automatic continuity conditions for finite-dimensional representations of connected Lie groups”, Russ. J. Math. Phys., 21:1 (2014), 133–134 | DOI | MR | Zbl

[38] A. I. Shtern, “Structure of finite-dimensional locally bounded finally precontinuous quasirepresentations of locally compact groups”, Russ. J. Math. Phys., 16:1 (2009), 133–138 | DOI | MR | Zbl

[39] A. I. Shtern, “Extension of pseudocharacters from normal subgroups”, Proc. Jangjeon Math. Soc., 18:4 (2015), 427–433 | MR | Zbl

[40] K. Iwasawa, “On some types of topological groups”, Ann. of Math. (2), 50:3 (1949), 507–558 | DOI | MR | Zbl