Quaternionic Lie algebras (Q799784)
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scientific article; zbMATH DE number 3873557
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quaternionic Lie algebras |
scientific article; zbMATH DE number 3873557 |
Statements
Quaternionic Lie algebras (English)
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1984
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Let k be a field of characteristic not equal to 2, and let L be a finite field extension of k. Then a Lie algebra G is quaternionic if there is a quaternion division algebra Q over L such that G is isomorphic to the k- Lie-algebra \(Q^-/L1\). The main theorem of the paper gives equivalent conditions for a finite-dimensional Lie algebra over a perfect field k to be quaternionic.
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quaternionic Lie algebra
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central quotient
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simple semiabelian
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Cartan subalgebras
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Fitting decomposition
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ad-semisimple
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characteristic not two
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quaternion division algebra
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