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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Main Authors:	Dzhumadil’daev A.S., Ismailov N.A., Orazgaliyev A.T.
Format:	Article
Language:	English
Published:	Sciendo 2020-09-01
Series:	Communications in Mathematics
Subjects:	diassociative algebars leibniz elements dynkin-specht-wever criterion 17a30 17a50
Online Access:	https://doi.org/10.2478/cm-2020-0017

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spelling	doaj-703fdf5b963e4a54836fe31a008f2ca12021-09-06T19:22:06ZengSciendoCommunications in Mathematics2336-12982020-09-0128215516010.2478/cm-2020-0017cm-2020-0017Lie commutators in a free diassociative algebraDzhumadil’daev A.S.0Ismailov N.A.1Orazgaliyev A.T.2Al-Farabi Kazakh National University, Almaty, Kazakhstan and Saint Petersburg State University, Saint Petersburg, RussiaAstana IT University, Nur-Sultan, Kazakhstan and Saint Petersburg State University, Saint Petersburg, RussiaInstitute of Mathematics and Mathematical Modeling, Almaty, KazakhstanWe 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.https://doi.org/10.2478/cm-2020-0017diassociative algebarsleibniz elementsdynkin-specht-wever criterion17a3017a50
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Dzhumadil’daev A.S. Ismailov N.A. Orazgaliyev A.T.
spellingShingle	Dzhumadil’daev A.S. Ismailov N.A. Orazgaliyev A.T. Lie commutators in a free diassociative algebra Communications in Mathematics diassociative algebars leibniz elements dynkin-specht-wever criterion 17a30 17a50
author_facet	Dzhumadil’daev A.S. Ismailov N.A. Orazgaliyev A.T.
author_sort	Dzhumadil’daev A.S.
title	Lie commutators in a free diassociative algebra
title_short	Lie commutators in a free diassociative algebra
title_full	Lie commutators in a free diassociative algebra
title_fullStr	Lie commutators in a free diassociative algebra
title_full_unstemmed	Lie commutators in a free diassociative algebra
title_sort	lie commutators in a free diassociative algebra
publisher	Sciendo
series	Communications in Mathematics
issn	2336-1298
publishDate	2020-09-01
description	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.
topic	diassociative algebars leibniz elements dynkin-specht-wever criterion 17a30 17a50
url	https://doi.org/10.2478/cm-2020-0017
work_keys_str_mv	AT dzhumadildaevas liecommutatorsinafreediassociativealgebra AT ismailovna liecommutatorsinafreediassociativealgebra AT orazgaliyevat liecommutatorsinafreediassociativealgebra
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Lie commutators in a free diassociative algebra

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