This article is cited in 9 scientific papers (total in 9 papers)
Algebraic theory of multi-valued formal groups
A. N. Kholodov
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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Mathematics of the USSR-Sbornik, 1982, 42:2, 265–285
MSC: Primary 13J05, 14L05; Secondary 22E99
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
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\paper Algebraic theory of multi-valued formal groups
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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This publication is cited in the following articles:
V. M. Buchstaber, A. N. Kholodov, “Topological constructions connected with many-valued formal groups”, Math. USSR-Izv., 20:1 (1983), 1–25
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
A. N. Kholodov, “Multidimensional two-valued commutative formal groups”, Russian Math. Surveys, 43:1 (1988), 243–244
A. N. Kholodov, “The umbral calculus on multivalued formal groups, and Adams projections in $K$-theory”, Math. USSR-Sb., 65:2 (1990), 423–437
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
Kholodov A., “The Umbral Calculus and Orthogonal Polynomials”, Acta Appl. Math., 19:1 (1990), 1–54
Kholodov A., “Formal Coalgebras and Applications”, J. Pure Appl. Algebr., 85:3 (1993), 271–310
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
V. M. Buchstaber, “$n$-valued groups: theory and applications”, Mosc. Math. J., 6:1 (2006), 57–84
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