A~Jordan algebra of a~Mal'tsev algebra
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 49-74.

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This paper is devoted to the generalization of the construction of a Jordan algebra of a Lie algebra and the known theorems on the local finite-dimensionality of Lie PI-algebras with an algebraic adjoint representation to Mal'tsev algebras.
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A. Yu. Golubkov. A~Jordan algebra of a~Mal'tsev algebra. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 49-74. http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a4/

[1] Beidar K. I., Mikhalev A. V., Slinko A. M., “Kriterii pervichnosti nevyrozhdennykh alternativnykh i iordanovykh algebr”, Tr. MMO, 50, 1987, 130–137 | Zbl

[2] Golubkov A. Yu., “Lokalnaya konechnost algebr”, Fundament. i prikl. matem., 19:6 (2014), 25–75

[3] Golubkov A. Yu., “Konstruktsii spetsialnykh radikalov algebr”, Fundament. i prikl. matem., 20:1 (2015), 57–133

[4] Golubkov A. Yu., “Radikal Kostrikina i podobnye emu radikaly algebr Li”, Fundament. i prikl. matem., 21:2 (2016), 157–180

[5] Golubkov A. Yu., “Algebraicheskie algebry Li ogranichennoi stepeni”, Fundament. i prikl. matem., 22:5 (2019), 209–242

[6] Dzhekobson H., Algebry Li, Mir, M., 1964

[7] Dzhekobson N., Stroenie kolets, Izd. inostr. lit., M., 1961

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

[9] Zhevlakov K. A., Shestakov I. P., “O lokalnoi konechnosti v smysle Shirshova”, Algebra i logika, 12:1 (1973), 41–73 | MR

[10] Zelmanov E. I., “Pervichnye iordanovy algebry. II”, Sib. matem. zhurn., 24:1 (1983), 89–104 | MR | Zbl

[11] Zelmanov E. I., “Algebry Li s algebraicheskim prisoedinennym predstavleniem”, Matem. sb., 121(163):4(8) (1983), 545–561 | MR

[12] Kostrikin A. I., Vokrug Bernsaida, Nauka, M., 1986 | MR

[13] Kuzmin E. N., “Algebraicheskie mnozhestva v algebrakh Maltseva”, Algebra i logika, 7:2 (1968), 42–47 | MR | Zbl

[14] Kuzmin E. N., “Algebry Maltseva i ikh predstavleniya”, Algebra i logika, 7:4 (1968), 48–59 | MR

[15] Kuzmin E. N., “Struktura i predstavleniya konechnomernykh algebr Maltseva”, Tr. In-ta mat. SO AN SSSR. Issled. po teor. kolets i algebr, 16 (1989), 75–101 | MR | Zbl

[16] Kuzmin E. N., Shestakov I. P., “Neassotsiativnye struktury”, Itogi nauki i tekhniki. Sovrem. probl. matem. Fundam. napravleniya, 57, 1990, 179–266

[17] Razmyslov Yu. P., Tozhdestva algebr i ikh predstavlenii, Nauka, M., 1989 | MR

[18] Filippov V. T., “O polupervichnykh algebrakh Maltseva kharakteristiki $3$”, Algebra i logika, 14:1 (1975), 100–111 | MR

[19] Filippov V. T., “Pervichnye algebry Maltseva”, Matem. zametki, 31:5 (1982), 669–678 | MR | Zbl

[20] Filippov V. T., “Ob engelevykh algebrakh Maltseva”, Algebra i logika, 15:1 (1976), 89–109 | MR | Zbl

[21] Filippov V. T., O nil-elementakh indeksa $2$ v algebrakh Maltseva, Dep. v VINITI. No 2499-80, 1980

[22] Filippov V. T., “Nil-elementy indeksa $2$ v algebrakh Maltseva”, Algebra i logika, 37:3 (1998), 358–373 | MR | Zbl

[23] Baxter W. E., Martindale W. S., 3rd., “Central closure of semiprime non-associative rings”, Commun. Algebra, 7:11 (1979), 1103–1132 | MR | Zbl

[24] Beidar K. I., Martindale W. B., 3rd, Mikhalev A. V., Rings with Generalized Identities, Marcel Dekker, New York, 1996 | MR | Zbl

[25] Brox J., García E., Gómez Lozano M., “Jordan algebras at Jordan elements of semiprime rings with involution”, J. Algebra, 468 (2016), 155–181 | MR | Zbl

[26] Brox J., Fernández López A., Gómez Lozano M., “Clifford elements in Lie algebras”, J. Lie Theory, 27:1 (2017), 283–296 | MR | Zbl

[27] Cabrera M., Fernández López A., Golubkov A. Yu., Moreno A., “Algebras whose multiplication algebra is PI or GPI”, J. Algebra, 459 (2016), 213–237 | MR | Zbl

[28] Ericson T. S., Martindale W. S., 3rd, Osborn J. M., “Prime non-associative algebras”, Pacific J. Math., 60:1 (1975), 49–63 | MR

[29] Fernández López A., García E., Gómez Lozano M., “The Jordan algebras of a Lie algebra”, J. Algebra, 308 (2007), 164–177 | MR | Zbl

[30] Fernández López A., Golubkov A. Yu., “Lie algebras with an algebraic adjoint representation revisited”, Manuscripta Math., 140:3 (2013), 363–376 | MR | Zbl

[31] Fernández López A., Jordan Structures in Lie Algebras, Mathematical Surveys and Monographs, Amer. Math. Soc., Providence, 2019 | MR | Zbl

[32] García E., Gómez Lozano M., “An elemental characterization of strong primeness in Lie algebras”, J. Algebra, 312 (2007), 132–141 | MR | Zbl

[33] García E., Gómez Lozano M., “A characterization of the Kostrikin radical of a Lie algebra”, J. Algebra, 346 (2011), 266–283 | MR | Zbl

[34] García E., Gómez Lozano M., “Nondegeneracy for Lie triple systems and Kantor pairs”, Can. Math. Bull., 54 (2011), 442–455 | MR | Zbl

[35] Loos O., “Über eine Beziehung zwischen Malcev-Algebren und Lie-Tripelsystemen”, Pacific J. Math., 18:3 (1966), 553–562 | MR | Zbl

[36] Sagle A. A., “Malcev algebras”, Trans. Amer. Math. Soc., 101:3 (1961), 426–458 | MR | Zbl

[37] Wisbauer R., Modules and algebras: Bimodule structure and group actions on algebras, Pitman Monographs Surveys Pure Appl. Math., 81, Longman, Harlow, 1996 | MR | Zbl