The problem of speciality of Malcev algebras

• Grant number: 18/03717-7
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: October 09, 2018
• End date: December 08, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Chestakov
• Grantee: Ivan Chestakov
• Visiting researcher: Sergey Sverchkov
• Visiting researcher institution: Russian Presidential Academy of National Economy and Public Administration (RANEPA), Russia
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 14/09310-5 - Algebraic structures and their representations, AP.TEM

Abstract

The main goal of suggested research project is to construct a counterexample to the Malcev problem about the veracity of the famous Poincare-Birkhoff-Witt theorem for Malcev algebras. The proposed approach to the construction is based on the adaptation of the famous Cohn Lemma from the theory of Jordan algebras for Malcev algebras. In order to construct a "Cohn element" in the free special Malcev algebra, we plan to define and investigate in this algebra certain analogues of "tetrad-eaters" used by E. Zelmanov also in the theory of Jodan algebras. Then a counter-example will be constructed as a quotient algebra by the ideal generated by a Cohn element. (AU)