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Mat. Sb., 1993, Volume 184, Number 10, Pages 53–66 (Mi msb1018)  

This article is cited in 1 scientific paper (total in 2 paper)

The smallest field of definition of a subgroup of the group $\mathrm{PSL}_2$

È. B. Vinberg


Abstract: As previously proved by the author, for each semisimple algebraic group of adjoint type that is dense in the Zariski topology there exists a smallest field of definition which is an invariant of the class of commensurable subgroups. In the present paper an algorithm is given for finding the smallest field of definition of a dense finitely generated subgroup of the group $\mathrm{PSL}_2(\mathbb{C})$. A criterion for arithmeticity of a lattice in $\mathrm{PSL}_2(\mathbb{R})$ or $\mathrm{PSL}_2(\mathbb{C})$ in terms of this field is presented.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 80:1, 179–190

Bibliographic databases:

UDC: 519.45
MSC: 20G15, 20G20
Received: 29.09.1992

Citation: È. B. Vinberg, “The smallest field of definition of a subgroup of the group $\mathrm{PSL}_2$”, Mat. Sb., 184:10 (1993), 53–66; Russian Acad. Sci. Sb. Math., 80:1 (1995), 179–190

Citation in format AMSBIB
\Bibitem{Vin93}
\by \`E.~B.~Vinberg
\paper The smallest field of definition of a~subgroup of the~group $\mathrm{PSL}_2$
\jour Mat. Sb.
\yr 1993
\vol 184
\issue 10
\pages 53--66
\mathnet{http://mi.mathnet.ru/msb1018}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1249413}
\zmath{https://zbmath.org/?q=an:0831.20061}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 80
\issue 1
\pages 179--190
\crossref{https://doi.org/10.1070/SM1995v080n01ABEH003519}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995QH35500009}


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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. 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
    2. D. Malinin, “On some characters of group representations”, Chebyshevskii sb., 20:2 (2019), 234–243  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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