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- Title
Centralizers of Linear and Locally Nilpotent Derivations.
- Authors
Bedratyuk, Leonid; Petravchuk, Anatolii; Chapovskyi, Evhen
- Abstract
Let 핂 be an algebraically closed field of characteristic zero, let 핂[x1,...,xn] be the polynomial algebra, and let Wn(핂) be the Lie algebra of all 핂-derivations on 핂[x1,...,xn]. For any derivation D with linear components, we describe the centralizer of D in Wn(핂) and propose an algorithm for finding the generators of this centralizer regarded as a module over the ring of constants of the derivation D in the case where D is a basic Weitzenböck derivation. In a more general case where a finitely generated integral domain A over the field 핂 is considered instead of the polynomial algebra 핂[x1,...,xn] and D is a locally nilpotent derivation on A, we prove that the centralizer CDerA(D) of D in the Lie algebra DerA of all 핂-derivations on A is a "large" subalgebra of Der A. Specifically, the rank of CDerA(D) over A is equal to the transcendence degree of the field of fractions Frac(A) over the field 핂.
- Subjects
INTEGRAL domains; LIE algebras; NILPOTENT Lie groups; ALGEBRA; POLYNOMIAL rings; POLYNOMIALS
- Publication
Ukrainian Mathematical Journal, 2024, Vol 75, Issue 8, p1190
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-023-02255-x