{"docId":9509,"paperId":9509,"url":"https:\/\/cm.episciences.org\/9509","doi":"10.2478\/cm-2020-0017","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":645,"name":"Volume 28 (2020), Issue 2 (Special Issue: 2nd International Workshop on Nonassociative Algebras in Porto)"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-03664992","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-03664992v1","dateSubmitted":"2022-05-11 15:41:14","dateAccepted":null,"datePublished":"2020-10-11 00:00:00","titles":{"en":"Lie commutators in a free diassociative algebra"},"authors":["Dzhumadil\u2019daev, A.S.","Ismailov, N.A.","Orazgaliyev, A.T."],"abstracts":{"en":"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."},"keywords":[["General Mathematics"],"[MATH]Mathematics [math]"]}