Geodesic
Algebraic aspects of the theory of multiplications in complex cobordism theory
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 55 (2000) no. 4, pp. 613-633

Voir la notice de l'article provenant de la source Math-Net.Ru

The general classiffication problem for stable associative multiplications in complex cobordism theory is considered. It is shown that this problem reduces to the theory of a Hopf algebra $S$ (the Landweber–Novikov algebra) acting on the dual Hopf algebra $S^*$ with distinguished "topologically integral" part $\Lambda$ that corresponds to the complex cobordism algebra of a point. We describe the formal group and its logarithm in terms of the algebra representations of $S$. The notion of one-dimensional representations of a Hopf algebra is introduced, and examples of such representations motivated by well-known topological and algebraic results are given. Divided-difference operators on an integral domain are introduced and studied, and important examples of such operators arising from analysis, representation theory, and non-commutative algebra are described. We pay special attention to operators of division by a non-invertible element of a ring. Constructions of new associative multiplications (not necessarily commutative) are given by using divided-difference operators. As an application, we describe classes of new associative products in complex cobordism theory. 
@article{RM_2000_55_4_a1,
     author = {B. I. Botvinnik and V. M. Buchstaber and S. P. Novikov and S. A. Yuzvinskii},
     title = {Algebraic aspects of the theory of multiplications in complex cobordism theory},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {613--633},
     publisher = {mathdoc},
     volume = {55},
     number = {4},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2000_55_4_a1/}
}
TY  - JOUR
AU  - B. I. Botvinnik
AU  - V. M. Buchstaber
AU  - S. P. Novikov
AU  - S. A. Yuzvinskii
TI  - Algebraic aspects of the theory of multiplications in complex cobordism theory
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2000
SP  - 613
EP  - 633
VL  - 55
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_2000_55_4_a1/
LA  - en
ID  - RM_2000_55_4_a1
ER  - 
%0 Journal Article
%A B. I. Botvinnik
%A V. M. Buchstaber
%A S. P. Novikov
%A S. A. Yuzvinskii
%T Algebraic aspects of the theory of multiplications in complex cobordism theory
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2000
%P 613-633
%V 55
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_2000_55_4_a1/
%G en
%F RM_2000_55_4_a1
B. I. Botvinnik; V. M. Buchstaber; S. P. Novikov; S. A. Yuzvinskii. Algebraic aspects of the theory of multiplications in complex cobordism theory. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 55 (2000) no. 4, pp. 613-633. http://geodesic.mathdoc.fr/item/RM_2000_55_4_a1/