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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 1, Pages 45–55 (Mi izv1912)  

This article is cited in 16 scientific papers (total in 17 papers)

Rings of definition of dense subgroups of semisimple linear groups

È. B. Vinberg

Abstract: We investigate the question: What is the smallest ring over which the elements of a dense subgroup (in the Zariski topology) of a emisimple algebraic group can be written down simultaneously for various rational linear representations?

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:1, 45–55

Bibliographic databases:

UDC: 519.4
MSC: Primary 20G05, 20G15; Secondary 22E40
Received: 16.03.1970

Citation: È. B. Vinberg, “Rings of definition of dense subgroups of semisimple linear groups”, Izv. Akad. Nauk SSSR Ser. Mat., 35:1 (1971), 45–55; Math. USSR-Izv., 5:1 (1971), 45–55

Citation in format AMSBIB
\by \`E.~B.~Vinberg
\paper Rings of definition of dense subgroups of semisimple linear groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 1
\pages 45--55
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 1
\pages 45--55

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Platonov, “The arithmetic theory of algebraic groups”, Russian Math. Surveys, 37:3 (1982), 1–62  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. T. N. Venkataramana, “On superrigidity and arithmeticity of lattices in semisimple groups over local fields of arbitrary characteristic”, Invent math, 92:2 (1988), 255  crossref  mathscinet  zmath  adsnasa  isi
    3. Giovanni Zanzotto, “On the material symmetry group of elastic crystals and the Born Rule”, Arch Rational Mech Anal, 121:1 (1992), 1  crossref  mathscinet  zmath
    4. È. B. Vinberg, “The smallest field of definition of a subgroup of the group $\mathrm{PSL}_2$”, Russian Acad. Sci. Sb. Math., 80:1 (1995), 179–190  mathnet  crossref  mathscinet  zmath  isi
    5. D. V. Alekseevskii, V. O. Bugaenko, G. I. Olshanskii, V. L. Popov, O. V. Schwarzman, “Érnest Borisovich Vinberg (on his 60th birthday)”, Russian Math. Surveys, 52:6 (1997), 1335–1343  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. Richard Pink, “Compact Subgroups of Linear Algebraic Groups”, Journal of Algebra, 206:2 (1998), 438  crossref
    7. V. V. Benyash-Krivets, “Decomposing finitely generated groups into free products with amalgamation”, Sb. Math., 192:2 (2001), 163–186  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Janez Bernik, “A generalization of Brauer's theorem on splitting fields to semigroups”, Journal of Algebra, 266:1 (2003), 162  crossref
    9. Mikhail Belolipetsky, Alexander Lubotzky, “Finite groups and hyperbolic manifolds”, Invent. math, 162:3 (2005), 459  crossref
    10. Vladimir L. Popov, Yuri G. Zarhin, “Finite linear groups, lattices, and products of elliptic curves”, Journal of Algebra, 305:1 (2006), 562  crossref
    11. Gopal Prasad, Andrei S. Rapinchuk, “Weakly commensurable arithmetic groups and isospectral locally symmetric spaces”, Publ math IHES, 2009  crossref  zmath  isi
    12. Gregor Masbaum, Alan W Reid, “All finite groups are involved in the mapping class group”, Geom. Topol, 16:3 (2012), 1393  crossref
    13. V.I.. Chernousov, A.S.. Rapinchuk, I.A.. Rapinchuk, “The genus of a division algebra and the unramified Brauer group”, Bull. Math. Sci, 2013  crossref
    14. Gopal Prasad, A.S.. Rapinchuk, “On the fields generated by the lengths of closed geodesics in locally symmetric spaces”, Geom Dedicata, 2013  crossref
    15. Kanghyun Choi, Suhyoung Choi, “The definability criteria for convex projective polyhedral reflection groups”, Geom Dedicata, 2014  crossref
    16. Belolipetsky M., “Arithmetic hyperbolic reflection groups”, Bull. Amer. Math. Soc., 53:3 (2016), 437–475  crossref  mathscinet  zmath  isi  elib  scopus
    17. Trans. Moscow Math. Soc., 78 (2017), 299–314  mathnet  crossref  elib
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