Zhas Galym
Руководитель: Mashurov F.А.
The goal of the project is a systematic study of polynomial identities that hold under mutation of various algebras, including perm algebras, bicommutative algebras, Novikov algebras, and Zinbiel algebras. We aim to understand the structural properties of algebras and to identify connections between them and non-associative algebras via differential (anti)commutator operations.
Expected results
Finding polynomial identities satisfied by a mutation of perm algebras. Describe all elements of a mutation in a free perm algebra. Construct a basis for a free mutation of a perm algebra. Studying homomorphic images of a mutation of a free perm algebra. Studying connections between perm algebras and non-associative algebras with respect to a differential (anti)commutator. Finding polynomial identities satisfied by a mutation of Zinbiel, Novikov, and bicommutative algebras. Description of mutation elements in free Novikov and bicommutative algebras.
The results obtained will be published in scientific journals included in quartiles in the Web of Science database, and (or) having a percentile according to CiteScore in the Scopus database and/or recommended by CQAES in the quantity and quality required in clause 7 of the competition documentation.
Team
Farukh Mashurov – Principal Investigator
Nurlan Ismailov – Scientific Advisor
Contacts
farukh.mashurov@sdu.edu.kz
Руководитель: Mashurov F.А.
The goal of the project is a systematic study of polynomial identities that hold under mutation of various algebras, including perm algebras, bicommutative algebras, Novikov algebras, and Zinbiel algebras. We aim to understand the structural properties of algebras and to identify connections between them and non-associative algebras via differential (anti)commutator operations.
Expected results
Finding polynomial identities satisfied by a mutation of perm algebras. Describe all elements of a mutation in a free perm algebra. Construct a basis for a free mutation of a perm algebra. Studying homomorphic images of a mutation of a free perm algebra. Studying connections between perm algebras and non-associative algebras with respect to a differential (anti)commutator. Finding polynomial identities satisfied by a mutation of Zinbiel, Novikov, and bicommutative algebras. Description of mutation elements in free Novikov and bicommutative algebras.
The results obtained will be published in scientific journals included in quartiles in the Web of Science database, and (or) having a percentile according to CiteScore in the Scopus database and/or recommended by CQAES in the quantity and quality required in clause 7 of the competition documentation.
Team
Farukh Mashurov – Principal Investigator
Nurlan Ismailov – Scientific Advisor
Contacts
farukh.mashurov@sdu.edu.kz
The goal of the project is a systematic study of polynomial identities that hold under mutation of various algebras, including perm algebras, bicommutative algebras, Novikov algebras, and Zinbiel algebras. We aim to understand the structural properties of algebras and to identify connections between them and non-associative algebras via differential (anti)commutator operations.
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