One-sided isotopes of finite-dimensional algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 3-16.

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

It is shown that the right isotopes of finite-dimensional $(-1,1)$-algebras cannot be reduced to left isotopes. It is proved that no unital isotope of the Mikheev algebra is a left alternative algebra. In particular, the opposite algebra, generally speaking, is not an isotope of the original algebra.
@article{FPM_2021_23_4_a0,
     author = {L. R. Borisova and V. I. Glizburg and S. V. Pchelintsev},
     title = {One-sided isotopes of finite-dimensional algebras},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {3--16},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a0/}
}
TY  - JOUR
AU  - L. R. Borisova
AU  - V. I. Glizburg
AU  - S. V. Pchelintsev
TI  - One-sided isotopes of finite-dimensional algebras
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2021
SP  - 3
EP  - 16
VL  - 23
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a0/
LA  - ru
ID  - FPM_2021_23_4_a0
ER  - 
%0 Journal Article
%A L. R. Borisova
%A V. I. Glizburg
%A S. V. Pchelintsev
%T One-sided isotopes of finite-dimensional algebras
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2021
%P 3-16
%V 23
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a0/
%G ru
%F FPM_2021_23_4_a0
L. R. Borisova; V. I. Glizburg; S. V. Pchelintsev. One-sided isotopes of finite-dimensional algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 3-16. http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a0/

[1] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR

[2] Maltsev A. I., “Ob odnom predstavlenii neassotsiativnykh kolets”, UMN, 7:1 (1952), 181–185 | MR | Zbl

[3] Pchelintsev S. V., “Nilpotentnost assotsiatornogo ideala svobodnogo konechnoporozhdennogo $(-1,1)$-koltsa”, Algebra i logika, 14:5 (1975), 543–571 | MR | Zbl

[4] Pchelintsev S. V., “O mnogoobrazii, porozhdennom svobodnoi algebroi tipa $(-1,1)$ s dvumya porozhdayuschimi”, Sib. matem. zhurn., 22:3 (1981), 162–178 | MR | Zbl

[5] Pchelintsev S. V., “Izotopy pervichnykh $(-1,1)$- i iordanovykh algebr”, Algebra i logika, 49:3 (2010), 388–423 | MR | Zbl

[6] Pchelintsev S. V., “Izotopy alternativnykh algebr kharakteristiki, otlichnoi ot $3$”, Izv. RAN. Ser. matem., 84:5 (2020), 197–210 | MR | Zbl

[7] Albert A. A., “Non-associative algebras”, Ann. Math., 43 (1942), 685–707 | MR | Zbl

[8] Allison B., Faulkner J., “Isotopy for extended affine Lie algebras and Lie tori”, Developments and Trends in Infinite-Dimensional Lie Theory, Progress Math., 288, eds. Neeb K.-H., Pianzola A., Birkhäuser, 2011, 3–43 | MR | Zbl

[9] Bruck R. H., “Some results in the theory of linear non-associative algebras”, Trans. Amer. Math. Soc., 56 (1944), 141–199 | MR | Zbl

[10] Darpö E., “Isotopes of Hurwitz algebras”, Mediterr. J. Math., 15 (2018), 52 | MR | Zbl

[11] Darpö E., Izquierdo J. M. P., “Autotopies and quasigroup identities: New aspects of non-associative division algebras”, Forum Math., 27:5 (2012), 2691–2745 | MR

[12] Falcón O. J., Falcón R. M., Núñez J., Isomorphism and isotopism classes of filiform Lie algebras of dimension up to seven, 2015, arXiv: 1510.07066 [math.RA] | MR

[13] Glizburg V. I., Pchelintsev S. V., “Isotopes of simple algebras of arbitrary dimension”, Asian-Eur. J. Math., 13:6 (2020), 2050108 | MR | Zbl

[14] Jacobson N., Structure and Representations of Jordan Algebras, Amer. Math. Soc. Colloq. Publ., 39, Amer. Math. Soc., 1968 | MR | Zbl

[15] Kleinfeld E., “Right alternative rings”, Proc. Amer. Math. Soc., 4 (1953), 939–944 | MR | Zbl

[16] Krylov A. A., Pchelintsev S. V., “Isotopic simple algebras with a nil basis”, Commun. Algebra, 48:4 (2020), 1697–1712 | MR | Zbl

[17] McCrimmon K., “Homotopes of alternative algebras”, Math. Ann., 191:4 (1971), 253–262 | MR | Zbl

[18] Schafer R. D., “Alternative algebras over an arbitrary filds”, Bull. Amer. Math. Soc., 49 (1943), 549–555 | MR | Zbl

[19] Schwarz T., “Small non-associative division algebras up to isotopy”, Algebra Discrete Math., 9 (2010), 103–108 | MR

[20] Thedy A., “Right alternative algebras and Wedderburn principal theorem”, Proc. Amer. Math. Soc., 72:3 (1978), 427–435 | MR | Zbl