Locally nilpotent Lie algebras of derivations of integral domains
Let K be a field of characteristic zero and A an integral domain over K. The Lie algebra DerKA of all K-derivations of A carries very important information about the algebra A. This Lie algebra is embedded into the Lie algebra RDerKA$\subseteq$DerKR, where R=Frac(A) is the fraction field of A. The r...
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| Date: | 2018 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine
2018
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| Subjects: | |
| Online Access: | http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/2457 |
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| Journal Title: | Prykladni Problemy Mekhaniky i Matematyky |
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Prykladni Problemy Mekhaniky i Matematyky| Summary: | Let K be a field of characteristic zero and A an integral domain over K. The Lie algebra DerKA of all K-derivations of A carries very important information about the algebra A. This Lie algebra is embedded into the Lie algebra RDerKA$\subseteq$DerKR, where R=Frac(A) is the fraction field of A. The rank rkRL of a subalgebra L of RDerKA is defined as dimension dimRRL. We prove that every locally nilpotent subalgebra L of RDerKA with rkRL=n has a series of ideals 0=L0⊂L1⊂L2…⊂Ln=L such that rkRLi=i and all the quotient Lie algebras Li+1⁄Li, i=0,…,n-1, are abelian. We also describe all maximal (with respect to inclusion) locally nilpotent subalgebras L of the Lie algebra RDerKA with rkRL=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. |
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