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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 1, Pages 214–226 (Mi izv1554)  

This article is cited in 18 scientific papers (total in 19 papers)

On some infinite-dimensional groups. II

I. R. Shafarevich


Abstract: This paper contains proofs of some previously announced theorems on infinitedimensional algebraic groups, and, in particular, on the structure of the group of automorphisms of an affine space as an infinite-dimensional algebraic group.
Bibliography: 9 titles.

Full text: PDF file (1418 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1982, 18:1, 185–194

Bibliographic databases:

Document Type: Article
UDC: 513.6
MSC: Primary 14L99; Secondary 20G99
Received: 23.09.1980

Citation: I. R. Shafarevich, “On some infinite-dimensional groups. II”, Izv. Akad. Nauk SSSR Ser. Mat., 45:1 (1981), 214–226; Math. USSR-Izv., 18:1 (1982), 185–194

Citation in format AMSBIB
\Bibitem{Sha81}
\by I.~R.~Shafarevich
\paper On~some infinite-dimensional groups.~II
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 1
\pages 214--226
\mathnet{http://mi.mathnet.ru/izv1554}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=607583}
\zmath{https://zbmath.org/?q=an:0491.14025|0475.14036}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 1
\pages 185--194
\crossref{https://doi.org/10.1070/IM1982v018n01ABEH001379}


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    Erratum

    This publication is cited in the following articles:
    1. S. P. Demushkin, A. I. Kostrikin, S. P. Novikov, A. N. Parshin, L. S. Pontryagin, A. N. Tyurin, D. K. Faddeev, “Igor' Rostislavovich Shafarevich (on his sixtieth birthday)”, Russian Math. Surveys, 39:1 (1984), 189–200  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Shrawan Kumar, “Demazure character formula in arbitrary Kac-Moody setting”, Invent math, 89:2 (1987), 395  crossref  mathscinet  zmath  isi
    3. Marilena Pittaluga, “On the group of automorphisms of a power series ring”, Journal of Algebra, 108:1 (1987), 34  crossref
    4. I. V. Artamkin, “Action of biregular automorphisms of the affine plane on pairs of matrices”, Math. USSR-Izv., 33:2 (1989), 433–439  mathnet  crossref  mathscinet  zmath
    5. Eiichi Abe, Mitsuhiro Takeuchi, “Groups associated with some types of infinite dimensional Lie algebras”, Journal of Algebra, 146:2 (1992), 385  crossref
    6. Zinovy Reichstein, “On automorphisms of matrix invariants induced from the trace ring”, Linear Algebra and its Applications, 193 (1993), 51  crossref
    7. Shrawan Kumar, M. S. Narasimhan, A. Ramanathan, “Infinite Grassmannians and moduli spaces ofG-bundles”, Math Ann, 300:1 (1994), 41  crossref  mathscinet  zmath  isi
    8. Indranil Biswas, Subhashis Nag, Dennis Sullivan, “Determinant bundles, Quillen metrics and Mumford isomorphisms over the universal commensurability Teichmüller space”, Acta Math, 176:2 (1996), 145  crossref  mathscinet  zmath  isi
    9. Proc. Steklov Inst. Math., 225 (1999), 141–147  mathnet  mathscinet  zmath
    10. I. R. Shafarevich, “On the Group $GL(2,K[t])$”, Proc. Steklov Inst. Math., 246 (2004), 308–314  mathnet  mathscinet  zmath
    11. Yu. Bodnarchuk, “Generating properties of biparabolic invertible polynomial maps in three variables”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, no. 1, 34–39  mathnet  mathscinet  zmath
    12. V. V. BAVULA, “THE GROUP OF AUTOMORPHISMS OF THE FIRST Weyl ALGEBRA IN PRIME CHARACTERISTIC AND THE RESTRICTION MAP”, Glasgow Math J, 2008, 1  crossref  mathscinet  isi
    13. J. Math. Sci. (N. Y.), 168:3 (2010), 428–436  mathnet  crossref
    14. Ronen Peretz, “On the Structure of the Semigroup of Entire Étale Mappings”, Complex Anal. Oper. Theory, 2013  crossref
    15. Jérémy Blanc, Jean-Philippe Furter, “Topologies and structures of the Cremona groups”, Ann. Math, 178:3 (2013), 1173  crossref
    16. V. L. Popov, “Tori in the Cremona groups”, Izv. Math., 77:4 (2013), 742–771  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. Kraft H., Russell P., “Families of Group Actions, Generic Isotriviality, and Linearization”, Transform. Groups, 19:3 (2014), 779–792  crossref  mathscinet  zmath  isi  scopus
    18. Kovalenko S. Perepechko A. Zaidenberg M., “On Automorphism Groups of Affine Surfaces”, Algebraic Varieties and Automorphism Groups, Advanced Studies in Pure Mathematics, 75, ed. Masuda K. Kishimoto T. Kojima H. Miyanishi M. Zaidenberg M., Math Soc Japan, 2017, 207–286  isi
    19. Trans. Moscow Math. Soc., 78 (2017), 171–186  mathnet  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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