Lie commutators in a free diassociative algebra

2020

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DOI 10.2478/cm-2020-0017
Data confidence 70 medium
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Abstract

Abstract 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.