On the speciality of Tortkara algebras

Author(s)

Dzhumadil'daev, A. S. ^[1] ; Ismailov, N. A. ^[2] ; Mashurov, F. A. ^[1]

Affiliation

^[1] Inst Math & Math Modeling, Alma Ata - Kazakhstan

^[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: Journal of Algebra; v. 540, p. 1-19, DEC 15 2019.
• Web of Science Citations: 0

Abstract

A criterion for elements of free Zinbiel algebras to be Lie or Jordan is established. This criterion is used in studying speciality problems of Tortkara algebras. We construct a base of free special Tortkara algebras. Furthermore, we prove analogues of classical Cohn's and Shirshov's theorems for Tortkara algebras. (C) 2019 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 17/21429-6 - The structure problems of Zinbiel-Lie and Novikov-Jordan algebras
• Grantee: Nurlan Ismailov
• Support Opportunities: Scholarships in Brazil - Post-Doctoral