Geodesic
Duisengaliyeva, B.A., Umirbaev, U.U.,
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1671-1679.

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

An example of a non-triangulable locally nilpotent derivation and an example of a wild exponential automorphism of the free Novikov algebra $N\left\langle x,y,z\right\rangle$ in three variables $x,y,z$ over a field of characteristic zero are constructed.
Keywords: differential polynomial algebra, free Novikov algebra, derivation
Mots-clés : automorphism. 
@article{SEMR_2018_15_a31,
     author = {B. A. Duisengaliyeva and U. U. Umirbaev},
     title = {Duisengaliyeva, {B.A.,} {Umirbaev,} {U.U.,}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1671--1679},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a31/}
}
TY  - JOUR
AU  - B. A. Duisengaliyeva
AU  - U. U. Umirbaev
TI  - Duisengaliyeva, B.A., Umirbaev, U.U.,
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 1671
EP  - 1679
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a31/
LA  - ru
ID  - SEMR_2018_15_a31
ER  - 
%0 Journal Article
%A B. A. Duisengaliyeva
%A U. U. Umirbaev
%T Duisengaliyeva, B.A., Umirbaev, U.U.,
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 1671-1679
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a31/
%G ru
%F SEMR_2018_15_a31
B. A. Duisengaliyeva; U. U. Umirbaev. Duisengaliyeva, B.A., Umirbaev, U.U.,. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1671-1679. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a31/

[1] H.W.E. Jung, “Uber ganze birationale Transformationen der Ebene”, J. Reine Angew. Math., 184 (1942), 161–174 | MR

[2] W. van der Kulk, “On polynomial rings in two variables”, Nieuw Arch. Wiskunde (3), 1 (1953), 33–41 | MR

[3] A.G. Czerniakiewicz, “Automorphisms of a free associative algebra of rank 2. I, II”, Trans. Amer. Math. Soc., 160 (1971), 393–401 ; 171 (1972), 309–315 | MR | MR

[4] Functional Anal. Appl., 4 (1970), 262–263 | DOI | MR

[5] L. Makar-Limanov, U. Turusbekova, U. Umirbaev, “Automorphisms and derivations of free Poisson algebras in two variables”, J. Algebra, 322:9 (2009), 3318–3330 | DOI | MR

[6] D. Kozybaev, L. Makar-Limanov, U. Umirbaev, “The Freiheitssatz and the automorphisms of free right-symmetric algebras”, Asian-European J. Math., 1:2 (2008), 243–254 | DOI | MR

[7] P.M. Cohn, “Subalgebras of free associative algebras”, Proc. London Math. Soc. (3), 14 (1964), 618–632 | DOI | MR

[8] U.U. Umirbaev, I.P. Shestakov, “Subalgebras and automorphisms of polynomial rings”, Dokl. Akad. Nauk, 386:6 (2002), 745–748 | MR

[9] U.U. Umirbaev, “Defining relations of the tame automorphism group of polynomial algebras and the wild automorphism of free associative algebras”, Dokl. RAN, 407:3 (2006), 319–324 | MR

[10] R. Rentschler, “Operations du groupe additif sur le plan”, C. R. Acad. Sci. Paris, 267 (1968), 384–387 | MR

[11] H. Bass, “A non-triangular action of $G_a$ on $A^3$”, J. of Pure and Appl. Algebra, 33:1 (1984), 1–5 | DOI | MR

[12] M. Nagata, On the automorphism group of $k[x, y]$, Kinokuniya, Kyoto Univ., Tokyo, 1972 | MR

[13] I.M. Gel'fand, I.Ya. Dorfman, “Hamiltonian operators and algebraic structures related to them”, Functional Analysis and Its Application, 13:4 (1979), 248–262 | DOI | MR

[14] A.S. Dzhumadil'daev, “Codimension growth and non-koszulity of Novikov operad”, Commun. Alg., 39 (2011), 2943–2952 | DOI | MR

[15] A.S. Dzhumadil'daev, C. Lofwall, “Trees, free right-simmetric algebras, free Novikov algebras and identities”, Homology, Homotopy and Applications, 4:2 (2002), 165–190 | DOI | MR

[16] L. Makar-Limanov, U. Umirbaev, “The Freiheitssatz for Novikov algebras”, TWMS J. Pure Appl. Math., 2 (2011), 228–235 | MR

[17] L.A. Bokut, Y. Chen, Z. Zhang, “Grobner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras”, J. Algebra Appl., 16:1 (2017), 1750001, 22 pp. | DOI | MR

[18] B.A. Duisengaliyeva, A.S. Naurazbekova, U.U. Umirbaev, Tame and wild automorphisms of differential polynomial algebras of rank 2 (to appear)

[19] E.R. Kolchin, Differential Algebra and Algebraic Groups, Pure and Applied Mathematics, Academic Press, New York–London, 1973 | MR