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 Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 5, Pages 944–970 (Mi izv1283)

Groups of formal diffeomorphisms of the superline, generating functions for sequences of polynomials, and functional equations

V. M. Buchstaber, A. N. Kholodov

Abstract: One of the goals in this article is to extend the umbral calculus to sequences of superpolynomials. A study is made of the group of formal diffeomorphisms of the superline and its main subgroups (the umbral group, the group of formal diffeomorphisms of the line). A complete description of the one-parameter subgroups is obtained, and a faithful supermatrix representation of this group is constructed. Homogeneous coalgebras on the line and superline are studied. The class of nondegenerate homogeneous coalgebras on the line is completely described. Functional equations that are connected with these coalgebras and generalize the classical functional equations of Cauchy, Pexider, Abel, Levi–Civita, and Stäkel are introduced and solved.
Bibliography: 30 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:2, 277–305

Bibliographic databases:

UDC: 512.81+517.58+517.965
MSC: Primary 05A40, 58A50; Secondary 14L05, 33A65
Revised: 31.10.1988

Citation: V. M. Buchstaber, A. N. Kholodov, “Groups of formal diffeomorphisms of the superline, generating functions for sequences of polynomials, and functional equations”, Izv. Akad. Nauk SSSR Ser. Mat., 53:5 (1989), 944–970; Math. USSR-Izv., 35:2 (1990), 277–305

Citation in format AMSBIB
\Bibitem{BucKho89} \by V.~M.~Buchstaber, A.~N.~Kholodov \paper Groups of formal diffeomorphisms of the superline, generating functions for sequences of polynomials, and functional equations \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1989 \vol 53 \issue 5 \pages 944--970 \mathnet{http://mi.mathnet.ru/izv1283} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1024450} \zmath{https://zbmath.org/?q=an:0731.33018} \transl \jour Math. USSR-Izv. \yr 1990 \vol 35 \issue 2 \pages 277--305 \crossref{https://doi.org/10.1070/IM1990v035n02ABEH000704} 

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This publication is cited in the following articles:
1. A. A. Bolibrukh, A. P. Veselov, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, S. P. Novikov, T. E. Panov, Yu. M. Smirnov, “Viktor Matveevich Buchstaber (on his 60th birthday)”, Russian Math. Surveys, 58:3 (2003), 627–635
2. I. K. Babenko, S. A. Bogatyi, “On the group of substitutions of formal power series with integer coefficients”, Izv. Math., 72:2 (2008), 241–264
3. E. Yu. Netay, “Geometric differential equations on bundles of Jacobians of curves of genus 1 and 2”, Trans. Moscow Math. Soc., 74 (2013), 281–292
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