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- W2757955967 abstract "Let K be a field of characteristic zero and A an integral domain over K . The Lie algebra Der K A of all K -derivations of A carries very important information about the algebra A . This Lie algebra is embedded into the Lie algebra R Der K A $subseteq$Der K R , where R =Frac( A ) is the fraction field of A . The rank rk R L of a subalgebra L of R Der K A is defined as dimension dim R RL . We prove that every locally nilpotent subalgebra L of R Der K A with rk R L = n has a series of ideals 0= L 0 ⊂ L 1 ⊂ L 2 …⊂ L n = L such that rk R L i = i and all the quotient Lie algebras L i +1 ⁄ L i , i =0,…, n -1, are abelian. We also describe all maximal (with respect to inclusion) locally nilpotent subalgebras L of the Lie algebra R Der K A with rk R L =3. Cite as: Petravchuk A. P., Shevchyk O. M., Sysak K. Ya . Locally nilpotent Lie algebras of derivations of integral domains // Appl. Probl. Mech. Math. – 2017. – No. 15. – С. 7–15." @default.
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- W2757955967 date "2018-04-04" @default.
- W2757955967 modified "2023-09-25" @default.
- W2757955967 title "Locally nilpotent Lie algebras of derivations of integral domains" @default.
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- W2757955967 doi "https://doi.org/10.15407/2457" @default.
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