Аннотация:
Пусть Φ – поле характеристики 0. Доказано, что правосимметричная ниль-алгебра
индекса n над Φ является правонильпотентной, а новиковская ниль-алгебра
индекса n над Φ – нильпотентной.
Библиография: 5 названий.
A. S. Panasenko, V. N. Zhelyabin, “Novikov 𝕑_{2}-Graded Algebras with an Associative 0-Component”, Sib Math J, 65:2 (2024), 426
Ivan Kaygorodov, Farukh Mashurov, Tran Giang Nam, Ze Rui Zhang, “Products of Commutator Ideals of Some Lie-admissible Algebras”, Acta. Math. Sin.-English Ser., 2024
Nurlan Ismailov, Ualbai Umirbaev, “On a variety of right-symmetric algebras”, Journal of Algebra, 658 (2024), 759
Vladimir Dotsenko, Nurlan Ismailov, Ualbai Umirbaev, “Polynomial identities in Novikov algebras”, Math. Z., 303:3 (2023)
Kaisar Tulenbaev, Ualbai Umirbaev, Viktor Zhelyabin, “On the Lie-solvability of Novikov algebras”, J. Algebra Appl., 22:05 (2023)
Alexandr Pozhidaev, Ualbai Umirbaev, Viktor Zhelyabin, “On simple left-symmetric algebras”, Journal of Algebra, 621 (2023), 58
Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev, “The algebraic classification of nilpotent Novikov algebras”, Filomat, 37:20 (2023), 6617
Umirbaev U., Zhelyabin V., “On the Solvability of Graded Novikov Algebras”, Int. J. Algebr. Comput., 31:07 (2021), 1405–1418
Zhelyabin V., Umirbaev U., “On the Solvability of Z(3)-Graded Novikov Algebras”, Symmetry-Basel, 13:2 (2021), 312
Shestakov I., Zhang Z., “Solvability and Nilpotency of Novikov Algebras”, Commun. Algebr., 48:12 (2020), 5412–5420
Zhang Z., Chen Yu., Bokut L.A., “Free Gelfand-Dorfman-Novikov Superalgebras and a Poincare-Birkhoff-Witt Type Theorem”, Int. J. Algebr. Comput., 29:3 (2019), 481–505
Artemovych O.D., Balinsky A.A., Blackmore D., Prykarpatski A.K., “Reduced Pre-Lie Algebraic Structures, the Weak and Weakly Deformed Balinsky-Novikov Type Symmetry Algebras and Related Hamiltonian Operators”, Symmetry-Basel, 10:11 (2018), 601
Bokut L.A., Chen Yu., Zhang Z., “Gr?bner?Shirshov bases method for Gelfand?Dorfman?Novikov algebras”, J. Algebra. Appl., 16:1 (2017), 1750001
Kozybaev D., Umirbaev U., “Identities of the left-symmetric Witt algebras”, Int. J. Algebr. Comput., 26:2 (2016), 435–450