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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 5, Pages 1100–1120 (Mi izv1600)  

This article is cited in 5 scientific papers (total in 5 papers)

The constructive theory of invariants

V. L. Popov


Abstract: In this paper we find an explicit upper bound on the number of elements of a minimal homogeneous system of generators of the algebra of invariants of an arbitrary connected semisimple linear group over an algebraically closed field of characteristic zero. We also show that the approach to the solution of this problem proposed by Dieudonné and Carrell contains an error and does not in fact achieve its aim.
Bibliography: 20 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:2, 359–376

Bibliographic databases:

UDC: 519.4
MSC: 15A72, 20G15
Received: 24.04.1981

Citation: V. L. Popov, “The constructive theory of invariants”, Izv. Akad. Nauk SSSR Ser. Mat., 45:5 (1981), 1100–1120; Math. USSR-Izv., 19:2 (1982), 359–376

Citation in format AMSBIB
\Bibitem{Pop81}
\by V.~L.~Popov
\paper The constructive theory of invariants
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 5
\pages 1100--1120
\mathnet{http://mi.mathnet.ru/izv1600}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=637618}
\zmath{https://zbmath.org/?q=an:0501.14006|0478.14006}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 2
\pages 359--376
\crossref{https://doi.org/10.1070/IM1982v019n02ABEH001422}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. L. Popov, “A finiteness theorem for representations with a free algebra of invariants”, Math. USSR-Izv., 20:2 (1983), 333–354  mathnet  crossref  mathscinet  zmath
    2. V. L. Popov, “Syzygies in the theory of invariants”, Math. USSR-Izv., 22:3 (1984), 507–585  mathnet  crossref  mathscinet  zmath
    3. V. F. Ignatenko, “On invariants of finite groups generated by reflections”, Math. USSR-Sb., 48:2 (1984), 551–563  mathnet  crossref  mathscinet  zmath
    4. Friedrich Knop, “Der kanonische modul eines invariantenrings”, Journal of Algebra, 127:1 (1989), 40  crossref
    5. Bertram Kostant, “On the centralizer of K in”, Journal of Algebra, 313:1 (2007), 252  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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