The structure problems of Zinbiel-Lie and Novikov-Jordan algebras

• Grant number: 17/21429-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2018
• End date: January 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Chestakov
• Grantee: Nurlan Ismailov
• 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 reserach project is concentrated in studing commutator algebras of Zinbiel Algebras (Lie-Zinbiel Algebras) and anti-commutator algebras of Novikov Algebras (Jordan-Novikov Algebras). We are interested in investigating identities for these Algebras and in studing of their homomorphic images. In case of Jordan-Novikov Algebras we want to determine whether this class forms a variety. Moreover, we pretend to find a criterion for an element of a free Novikov Algebra to be a Jordan element. Representations of symmetric group on free Algebras of both types will be studied. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ISMAILOV, NURLAN; KAYGORODOV, IVAN; VOLKOV, YURY. Degenerations of Leibniz and Anticommutative Algebras. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, v. 62, n. 3, p. 539-549, SEP 2019. (17/21429-6, 17/15437-6)

ARINKIN, DIMA; CALDARARU, ANDREI; HABLICSEK, MARTON. Formality of derived intersections and the orbifold HKR isomorphism. Journal of Algebra, v. 540, p. 100-120, DEC 15 2019. (17/21429-6)

DZHUMADIL'DAEV, A. S.; ISMAILOV, N. A.; MASHUROV, F. A.. On the speciality of Tortkara algebras. Journal of Algebra, v. 540, p. 1-19, DEC 15 2019. (17/21429-6)