Lie commutators in a free diassociative algebra

Lie commutators in a free diassociative algebra

We give a criterion for Leibniz elements in a free diassociative algebra. In the diassociative case one can consider two versions of Lie commutators. We give criterions for elements of diassociative algebras to be Lie under these commutators. One of them corresponds to Leibniz elements. It generaliz...

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Veröffentlicht in:Communications in Mathematics 2020-09, Vol.28 (2), p.155-160
Hauptverfasser: Dzhumadil’daev, A.S., Ismailov, N.A., Orazgaliyev, A.T.
Format: Artikel
Sprache:eng
Schlagworte:
17A30
17A50
Diassociative algebars
Dynkin-Specht-Wever criterion
Leibniz elements
Mathematics
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Zusammenfassung:We give a criterion for Leibniz elements in a free diassociative algebra. In the diassociative case one can consider two versions of Lie commutators. We give criterions for elements of diassociative algebras to be Lie under these commutators. One of them corresponds to Leibniz elements. It generalizes the Dynkin-Specht-Wever criterion for Lie elements in a free associative algebra.
ISSN:2336-1298
1804-1388
2336-1298
DOI:10.2478/cm-2020-0017