Yefimov D. Centralizers of elements in Lie algebras of derivations of polynomial rings

Українська версія

Thesis for the degree of Doctor of Philosophy (PhD)

State registration number

0824U002893

Thesis Registration Form

0824U002893.pdf

Applicant for

Specialization

  • 111 - Математика

26-08-2024

Specialized Academic Board

5319

Taras Shevchenko National University of Kyiv

Essay

The dissertation is devoted to studying subalgebras and centralizers of elements in Lie algebras of derivations of polynomial rings over algebraically closed field of characteristic zero. Key words: derivation, Jacobian derivation, linear derivation, centralizer of a derivation, field of constants, Lie algebra, locally nilpotent Lie algebra, solvable Lie algebra, general linear Lie algebra, general affine Lie algebra, polynomial ring, ideal, triangular Lie algebra, maximal solvable subalgebra, closed polynomial.

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Research papers

Chapovskyi, Y., Efimov, D., Petravchuk, A.: Centralizers of elements in Lie algebras of vector fields with polynomial coefficients. Proc. Int. Geom. Cent. 14(4), 257–270 (2022).

Chapovskyi, Y. Y., Efimov, D. I., Petravchuk, A. P.: Solvable Lie algebras of derivations of polynomial rings in three variables. Прикл. проблеми механiки i математики 16, 7–13 (2018).

Efimov, D. I., Petravchuk, A. P., Sydorov, M. S.: Centralizers of Jacobian derivations. Algebra Discrete Math. 36(1), 22-31 (2023).

Efimov, D. I., Sydorov, M. S., Sysak, K. Ya.: On maximality of some solvable and locally nilpotent subalgebras of the Lie algebra 𝑊𝑛(𝐾). Res. Math. 31(2), 27-35 (2023).

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Files

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