Abstract:
We prove an analogue of the Bergen–Herstein–Lanski theorem for alternative
algebras: describe all alternative algebras that admit derivations with
invertible values. We also prove an analogue of Moens' theorem for alternative
algebras (a finite-dimensional alternative algebra over a field
of characteristic zero is nilpotent if and only if it admits an invertible
Leibniz derivation).
Keywords:
derivation, alternative algebra, nilpotent algebra.
Citation:
I. B. Kaygorodov, Yu. S. Popov, “Alternative algebras admitting derivations with invertible values and invertible derivations”, Izv. Math., 78:5 (2014), 922–936
This publication is cited in the following 18 articles:
S. V. Pchelintsev, M. S. Dubrovin, “Derivations of simple three-dimensional anticommutative algebras”, Zhurn. Belorus. gos. un-ta. Matem. Inf., 2 (2024), 19–26
Nejib Saadaoui, Sergei Silvestrov, Springer Proceedings in Mathematics & Statistics, 426, Non-commutative and Non-associative Algebra and Analysis Structures, 2023, 761
Ferreira Bruno Leonardo Macedo, Kaygorodov I., “Commuting Maps on Alternative Rings”, Ric. Mat., 71:1 (2022), 67–78
B. L. M. Ferreira, G. C. De Moraes, “Generalized Lie-type derivations of alternative algebras”, Russian Math. (Iz. VUZ), 65:9 (2021), 33–40
Abdaoui E., Mabrouk S., Makhlouf A., Massoud S., “Yau-Type Ternary Hom-Lie Bialgebras”, Turk. J. Math., 45:3 (2021), 1209–1240
K.K. Abdurasulov, A. Kh. Khudoyberdiyev, M. Ladra, A.M. Sattarov, “Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras”, Communications in Mathematics, 29:2 (2021), 187
Devi G.L., Jayalakshmi K., “Derivations With Invertible Values in Flexible Algebras”, Bol. Soc. Parana. Mat., 38:6 (2020), 63–71
Macedo Ferreira B.L., Guzzo Jr H., Ferreira R.N., Wei F., “Jordan Derivations of Alternative Rings”, Commun. Algebr., 48:2 (2020), 717–723
Macedo Ferreira B.L., Guzzo Jr. Henrique, Wei F., “Multiplicative Lie-Type Derivations on Alternative Rings”, Commun. Algebr., 48:12 (2020), 5396–5411
Artemovych O.D., Bovdi V.A., Salim M.A., “Derivations of Group Rings”, Acta Sci. Math., 86:1-2 (2020), 51–72
I. Kaygorodov, A. Lopatin, Yu. Popov, “Jordan algebras admitting derivations with invertible values”, Comm. Algebra, 46:1 (2018), 69–81
I. Kaygorodov, A. Lopatin, Yu. Popov, “The structure of simple noncommutative Jordan superalgebras”, Mediterr. J. Math., 15:2 (2018), UNSP 33, 20 pp.
V. N. Zhelyabin, A. I. Shestakov, “Alternative and Jordan algebras admitting ternary derivations with invertible values”, Sib. elektron. matem. izv., 14 (2017), 1505–1523
I. Kaygorodov, “On the Kantor product”, J. Algebra Appl., 16:9 (2017), 1750167, 17 pp.
I. Kaygorodov, Yu. Popov, “Generalized derivations of (color) n-ary algebras”, Linear and Multilinear Algebra, 64:6 (2016), 1086–1106
I. Kaygorodov, Yu. Popov, “A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations”, J. Algebra, 456 (2016), 323–347
I. Kaygorodov, E. Okhapkina, “δ-Derivations of semisimple finite-dimensional structurable algebras”, J. Algebra and Appl., 13:4 (2014), 1350130, 12 pp.
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