On nilpotent Lie algebras of derivations with large center
Let \(\mathbb K\) be a field of characteristic zero and \(A\) an associative commutative \(\mathbb K\)-algebra that is an integral domain. Denote by \(R\) the quotient field of \(A\) and by \(W(A)=R\operatorname{Der} A\) the Lie algebra of derivations on \(R\) that are products of elements of \(R\)...
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| Date: | 2016 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2016
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/132 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | Let \(\mathbb K\) be a field of characteristic zero and \(A\) an associative commutative \(\mathbb K\)-algebra that is an integral domain. Denote by \(R\) the quotient field of \(A\) and by \(W(A)=R\operatorname{Der} A\) the Lie algebra of derivations on \(R\) that are products of elements of \(R\) and derivations on \(A\). Nilpotent Lie subalgebras of the Lie algebra \(W(A)\) of rank \(n\) over \(R\) with the center of rank \(n-1\) are studied. It is proved that such a Lie algebra \(L\) is isomorphic to a subalgebra of the Lie algebra \(u_n(F)\) of triangular polynomial derivations where \(F\) is the field of constants for \(L\). |
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