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Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 1, Pages 3–25 (Mi izv1102)  

This article is cited in 17 scientific papers (total in 18 papers)

On certain commutative subalgebras of a universal enveloping algebra

È. B. Vinberg


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English version:
Mathematics of the USSR-Izvestiya, 1991, 36:1, 1–22

Bibliographic databases:

UDC: 519.46
MSC: Primary 17B35; Secondary 17B10
Received: 16.08.1989

Citation: È. B. Vinberg, “On certain commutative subalgebras of a universal enveloping algebra”, Izv. Akad. Nauk SSSR Ser. Mat., 54:1 (1990), 3–25; Math. USSR-Izv., 36:1 (1991), 1–22

Citation in format AMSBIB
\Bibitem{Vin90}
\by \`E.~B.~Vinberg
\paper On certain commutative subalgebras of a universal enveloping algebra
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1990
\vol 54
\issue 1
\pages 3--25
\mathnet{http://mi.mathnet.ru/izv1102}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1044045}
\zmath{https://zbmath.org/?q=an:0714.17009}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..36....1V}
\transl
\jour Math. USSR-Izv.
\yr 1991
\vol 36
\issue 1
\pages 1--22
\crossref{https://doi.org/10.1070/IM1991v036n01ABEH001925}


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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. A. A. Tarasov, “On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $\mathfrak{gl}(n,\mathbb C)$”, Sb. Math., 191:9 (2000), 1375–1382  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. V. Shuvalov, “On Limits of Mishchenko–Fomenko Subalgebras in Poisson Algebras of Semisimple Lie Algebras”, Funct. Anal. Appl., 36:4 (2002), 298–305  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. A. A. Tarasov, “The maximality of certain commutative subalgebras in the Poisson algebra of a semisimple Lie algebra”, Russian Math. Surveys, 57:5 (2002), 1013–1014  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. A. A. Tarasov, “Uniqueness of liftings of maximal commutative subalgebras of the Poisson–Lie algebra to the enveloping algebra”, Sb. Math., 194:7 (2003), 1105–1111  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Serge Ovsienko, “Strongly nilpotent matrices and Gelfand–Zetlin modules”, Linear Algebra and its Applications, 365 (2003), 349  crossref
    7. L. G. Rybnikov, “Centralizers of certain quadratic elements in Poisson–Lie algebras and the method of translation of invariants”, Russian Math. Surveys, 60:2 (2005), 367–369  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. L. G. Rybnikov, “The Argument Shift Method and the Gaudin Model”, Funct. Anal. Appl., 40:3 (2006), 188–199  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. Boris Feigin, Michael Finkelberg, Igor Frenkel, Leonid Rybnikov, “Gelfand–Tsetlin algebras and cohomology rings of Laumon spaces”, Sel. Math. New Ser, 2010  crossref
    10. Apoorva Khare, Tim Ridenour, “Faces of Weight Polytopes and a Generalization of a Theorem of Vinberg”, Algebr Represent Theor, 2010  crossref
    11. B. Feigin, E. Frenkel, V. Toledano Laredo, “Gaudin models with irregular singularities”, Advances in Mathematics, 223:3 (2010), 873  crossref
    12. Vyacheslav Futorny, Serge Ovsienko, Manuel Saorín, “Torsion theories induced from commutative subalgebras”, Journal of Pure and Applied Algebra, 2011  crossref
    13. Math. Notes, 90:5 (2011), 666–677  mathnet  crossref  crossref  mathscinet  isi
    14. Rocco Chirivì, “Root polytope and partitions”, J Algebr Comb, 2014  crossref
    15. P. Cellini, M. Marietti, “Root Polytopes and Borel Subalgebras”, International Mathematics Research Notices, 2014  crossref
    16. È. B. Vinberg, “Limits of Integrable Hamiltonians on Semisimple Lie Algebras”, Funct. Anal. Appl., 48:2 (2014), 107–115  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    17. Vyacheslav Futorny, Dimitar Grantcharov, Luis Enrique Ramirez, “Irreducible Generic Gelfand–Tsetlin Modules of $\mathfrak{gl}(n)$”, SIGMA, 11 (2015), 018, 13 pp.  mathnet  crossref  mathscinet
    18. Trans. Moscow Math. Soc., 78 (2017), 217–234  mathnet  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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