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On analogs of some group-theoretic concepts and results for Leibniz algebras
An algebra L over a field F is said to be a Leibniz algebra (more precisely a left Leibniz algebra) if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] – [b, [a, c]] for all a, b, c ∈ L. Leibniz algebras are generalizations of Lie algebras. We consider some classes of generalized nilpo...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Видавничий дім "Академперіодика" НАН України
2018
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| Series: | Доповіді НАН України |
| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/132403 |
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| Summary: | An algebra L over a field F is said to be a Leibniz algebra (more precisely a left Leibniz algebra) if it satisfies the
Leibniz identity: [[a, b], c] = [a, [b, c]] – [b, [a, c]] for all a, b, c ∈ L. Leibniz algebras are generalizations of Lie algebras.
We consider some classes of generalized nilpotent Leibniz algebras (hypercentral, locally nilpotent algebras,
and algebras with the idealizer condition) and show their some basic properties. |
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