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Mat. Sb. (N.S.), 1981, Volume 114(156), Number 2, Pages 299–321 (Mi msb2326)  

This article is cited in 9 scientific papers (total in 9 papers)

Algebraic theory of multi-valued formal groups

A. N. Kholodov


Abstract: This paper deals with the algebraic theory of multi-valued formal groups. The letters FG will be used to mean an $n$-valued formal group.
It is shown that to any FG there corresponds a coalgebra of a certain form. The form of the generator of an FG is obtained, and differential equations involving the coefficients of the generator are derived. It is shown that an FG can be uniquely reproduced by its generator. The generator of a cyclic elementary group is computed. A classification is obtained for the three-valued, four-valued, and five-valued FG's. It is proved that there exist finitely many elementary FG's with order not greater than 11.
Bibliography: 4 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 42:2, 265–285

Bibliographic databases:

UDC: 513.836
MSC: Primary 13J05, 14L05; Secondary 22E99
Received: 03.12.1979

Citation: A. N. Kholodov, “Algebraic theory of multi-valued formal groups”, Mat. Sb. (N.S.), 114(156):2 (1981), 299–321; Math. USSR-Sb., 42:2 (1982), 265–285

Citation in format AMSBIB
\Bibitem{Kho81}
\by A.~N.~Kholodov
\paper Algebraic theory of multi-valued formal groups
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 114(156)
\issue 2
\pages 299--321
\mathnet{http://mi.mathnet.ru/msb2326}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=609292}
\zmath{https://zbmath.org/?q=an:0485.14010|0474.14029}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 42
\issue 2
\pages 265--285
\crossref{https://doi.org/10.1070/SM1982v042n02ABEH002253}


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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. M. Buchstaber, A. N. Kholodov, “Topological constructions connected with many-valued formal groups”, Math. USSR-Izv., 20:1 (1983), 1–25  mathnet  crossref  mathscinet  zmath
    2. Kholodov A., “Classification of 6-Valued, 7-Valued and 8-Valued Elementary Formal Groups”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1984, no. 1, 30–33  mathscinet  zmath  isi
    3. A. N. Kholodov, “Multidimensional two-valued commutative formal groups”, Russian Math. Surveys, 43:1 (1988), 243–244  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. N. Kholodov, “The umbral calculus on multivalued formal groups, and Adams projections in $K$-theory”, Math. USSR-Sb., 65:2 (1990), 423–437  mathnet  crossref  mathscinet  zmath
    5. V. M. Buchstaber, A. N. Kholodov, “Groups of formal diffeomorphisms of the superline, generating functions for sequences of polynomials, and functional equations”, Math. USSR-Izv., 35:2 (1990), 277–305  mathnet  crossref  mathscinet  zmath
    6. Kholodov A., “The Umbral Calculus and Orthogonal Polynomials”, Acta Appl. Math., 19:1 (1990), 1–54  mathscinet  zmath  isi
    7. Kholodov A., “Formal Coalgebras and Applications”, J. Pure Appl. Algebr., 85:3 (1993), 271–310  crossref  mathscinet  zmath  isi
    8. B. I. Botvinnik, V. M. Buchstaber, S. P. Novikov, S. A. Yuzvinskii, “Algebraic aspects of the theory of multiplications in complex cobordism theory”, Russian Math. Surveys, 55:4 (2000), 613–633  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. V. M. Buchstaber, “$n$-valued groups: theory and applications”, Mosc. Math. J., 6:1 (2006), 57–84  mathnet  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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