Geodesic
Hopf algebras of linear recurring sequences
Diskretnaya Matematika, Tome 16 (2004) no. 2, pp. 7-43.

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

It is known that the algebra of linear recurring sequences over a commutative ring $R$ is the Hopf algebra dual to the polynomial algebra over $R$. In this paper, we consider some concepts and operations of the theory of Hopf algebras and modules which have interesting interpretations in terms of linear recurring sequences.This research was supported by the President of the Russian Federation grants 2358.2003.9 for support of leading scientific schools and 2452.2004.10 for support of young doctors of sciences. 
@article{DM_2004_16_2_a1,
     author = {V. L. Kurakin},
     title = {Hopf algebras of linear recurring sequences},
     journal = {Diskretnaya Matematika},
     pages = {7--43},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2004_16_2_a1/}
}
TY  - JOUR
AU  - V. L. Kurakin
TI  - Hopf algebras of linear recurring sequences
JO  - Diskretnaya Matematika
PY  - 2004
SP  - 7
EP  - 43
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2004_16_2_a1/
LA  - ru
ID  - DM_2004_16_2_a1
ER  - 
%0 Journal Article
%A V. L. Kurakin
%T Hopf algebras of linear recurring sequences
%J Diskretnaya Matematika
%D 2004
%P 7-43
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2004_16_2_a1/
%G ru
%F DM_2004_16_2_a1
V. L. Kurakin. Hopf algebras of linear recurring sequences. Diskretnaya Matematika, Tome 16 (2004) no. 2, pp. 7-43. http://geodesic.mathdoc.fr/item/DM_2004_16_2_a1/

[1] Artamonov V. A., “Stroenie algebr Khopfa”, Itogi nauki i tekhniki. Algebra, geometriya, topologiya, 29, 1991, 3–63 | MR

[2] Bakhturin Yu. A., Osnovnye struktury sovremennoi algebry, Nauka, Moskva, 1990 | MR | Zbl

[3] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, ch. II, Gelios, Moskva, 2003

[4] Kurakin V. L., “Konvolyutsiya lineinykh rekurrentnykh posledovatelnostei”, Uspekhi matem. nauk, 48:4 (1993), 235–236 | MR | Zbl

[5] Kurakin V. L., “Stroenie algebr Khopfa lineinykh rekurrentnykh posledovatelnostei”, Uspekhi matem. nauk, 48:5 (1993), 177–178 | MR | Zbl

[6] Kurakin V. L., “Algebry Khopfa lineinykh rekurrentnykh posledovatelnostei nad kommutativnymi koltsami”, Trudy Vtorykh matematicheskikh chtenii MGSU, Moskva, 1994, 67–69

[7] Kurakin V. L., “Algebra Khopfa, dualnaya k algebre mnogochlenov nad kommutativnym koltsom”, Matem. zametki, 71:5 (2002), 677–685 | MR | Zbl

[8] Lidl R. Niderraiter G., Konechnye polya t. 2, Mir, Moskva, 1988 | Zbl

[9] Tsirler N., “Lineinye vozvratnye posledovatelnosti”, Kibern. sb., 6 (1963), 55–79

[10] Abe E., Hopf algebras, Cambridge Univ. Press, Cambridge, 1980 | MR | Zbl

[11] Abuhlail J. Y., Gómez-Torrecillas J., Wisbauer R., “Dual coalgebras of algebras over commutative rings”, J. Pure and Appl. Algebra, 153 (2000), 107–120 | DOI | MR | Zbl

[12] Abuhlail J. Y., Gómez-Torrecillas J., Lobillo F., “Duality and rational modules in Hopf algebras over commutative rings”, J. Algebra, 240 (2001), 165–184 | DOI | MR | Zbl

[13] Cerlienco L., Piras F., “On the continuous dual of a polynomial bialgebra”, Commun. Algebra, 19:10 (1991), 2707–2727 | DOI | MR | Zbl

[14] Cerruti U., Vaccarino F., “$R$-algebras of linear recurrent sequences”, J. Algebra, 175 (1995), 332–338 | DOI | MR | Zbl

[15] Chin W., Goldman J., “Bialgebras of lineary recursive sequences”, Commun. Algebra, 21:11 (1993), 3935–3952 | DOI | MR | Zbl

[16] Haukkanen P., “On a convolution of linear recurring sequences over finite fields. I, II”, J. Algebra, 149:1 (1992), 179–182 ; 164:2 (1994), 542–544 | DOI | MR | Zbl | DOI | MR | Zbl

[17] Kurakin V. L., Kuzmin A. S., Mikhalev A. V., Nechaev A. A., “Linear recurring sequences over rings and modules”, J. Math. Sci., 76:6 (1995), 2793–2915 | DOI | MR | Zbl

[18] Kurakin V. L., Mikhalev A. V., Nechaev A. A., Tsypyschev V. N., “Linear and polylinear recurring sequences over abelian groups and modules”, J. Math. Sci., 102:6 (2000), 4598–4627 | MR

[19] Kurakin V. L., Nechaev A. A., “Quasi-Frobenius bimodules of functions on a semigroup”, Commun. Algebra, 29:9 (2001), 4079–4094 | DOI | MR | Zbl

[20] Larson R., Taft E. Y., “The algebraic structure of linearly recursive sequences under Hadamard product”, Israel J. Math., 72 (1990), 118–132 | DOI | MR | Zbl

[21] Montogomery S., Hopf algebras and their actions on rings, Amer. Math. Soc., Providence, 1993

[22] Peterson B., Taft E. Y., “The Hopf algebra of linear recursive sequences”, Aequat. Math., 20 (1980), 1–17 | DOI | MR | Zbl

[23] Snapper E., “Completely primary rings, I”, Ann. Math., 52:3 (1950), 666–693 | DOI | MR

[24] Sweedler M. F., Hopf algebras, 1969, Benjamin, New York | MR | Zbl

[25] Taft E., “Algebraic aspects of linearly recursive sequences”, Lect. Notes Pure Appl. Math., 158, 1994, 299–317 | MR | Zbl

[26] Taft E., “Linearly recursive tableaux”, Congr. Numerantium, 107 (1995), 33–36 | MR | Zbl

[27] Zierler N., Mills W. H., “Products of linear recurring sequences”, J. Algebra, 27:1 (1973), 147–157 | DOI | MR | Zbl