Triple sums of abelian Lie algebras |
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| Author |
Kyiv University
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| Abstract |
For a Lie algebra $L$ (over an arbitrary field)
of the form $L=A+B=A+N=B+N$ with
abelian subalgebras $A$, $B$ and an~abelian ideal $N$. We construct
an associative algebra $R$ over the~same field
such that the adjoint Lie algebra $R^{(-)}$ is isomorphic
to $L$. Applying the~structure results for associative algebras
we prove that in finite dimensional case such a~Lie algebra
$L$ contains a nilpotent ideal $I$ such that $L/I$ is
the~direct product of nonabelian two-dimensional Lie algebras.
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| Keywords |
Lie algebra, abelian subalgebras, abelian ideal, associative algebra, adjoint Lie algebra
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| DOI |
doi:10.30970/ms.8.1.11-14
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Reference |
1. O.H. Kegel Zur Struktur mehrfach faktorisierbarer endlicher Gruppen // Math. Z.–1965 N.87 p.42–48
2. Yu.A. Drozd, V.V.Kirichenko Finite dimensional algebras ,addr Berlin–Heidelberg–New-York–London–1994250 3. Y.P. Sysak Products of infinite groups// Akad. Nauk Ukrainy, Inst. Mat. Kiev, Preprint 82.53–1982Russian 4. A.P. Petravchuk On triple sums of abelian Lie algebras // Abstracts of 5-th International Mathematical Conference in memory of acad. M. Kravchuk, Kiev–1996 |
| Pages |
11-14
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| Volume |
8
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| Issue |
1
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| Year |
1997
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| Journal |
Matematychni Studii
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| Full text of paper | |
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