On the speciality of Tortkara algebras
Askar Dzhumadil'daev, Nurlan Ismailov, Farukh Mashurov
TL;DR
This paper establishes criteria for elements in free Zinbiel algebras to be Lie or Jordan, and applies these to study the structure and special properties of Tortkara algebras, including bases and classical theorems.
Contribution
It introduces a criterion for element classification in free Zinbiel algebras and constructs bases for free special Tortkara algebras, extending classical theorems to this context.
Findings
Established a criterion for Lie or Jordan elements in free Zinbiel algebras
Constructed a basis for free special Tortkara algebras
Proved analogues of Cohn's and Shirshov's theorems for Tortkara algebras
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.
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