Subalgebras of differential algebras with respect to new multiplications Бауыржан Каирбекович Сартаев

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Бауыржан, Каирбекович Сартаев.
Подалгебры дифференциальных алгебр относительно новых умножений = Subalgebras of differential algebras with respect to new multiplications : Subalgebras of differential algebras with respect to new multiplications : диссертация ... кандидата физико-математических наук : 01.01.06 / Бауыржан Каирбекович Сартаев; [Место защиты: ФГАОУ ВО «Новосибирский национальный исследовательский государственный университет» ; Диссовет Совет по защите диссертаций по математическим наукам]. - Новосибирск, 2023. - 94 с.
Оглавление диссертациикандидат наук Бауыржан Каирбекович Сартаев
Contents
1 Introduction
1.1 General description of the work
1.1.1 The goal of research
1.1.2 General methodology of the research
1.1.3 Scientific novelty
1.1.4 Theoretical and practical significance
1.1.5 Publications
1.1.6 The structure and scope of the thesis
1.1.7 Acknowledgements
2 Differential Poisson algebras
2.1 Preliminaries on the special GD-algebras
2.2 Special GD-algerbas
2.3 Special identities of GD-algebras
2.4 On the Grobner basis of the Gelfand-Dorfman operad with special identities
3 Differential associative algebras
3.1 Preliminaries on the Novikov and noncommutative Novikov algebras
3.2 Basic notions on the differential associative algebra
3.3 Free noncommutative Novikov algebra
3.4 Embedding into differential algebras
3.5 Alternative proof of Theorem
4 Differential perm algebras
4.1 Preliminaries on the left symmetric algebras
4.2 Novikov dialgebras and differential perm algebras
4.3 Universal enveloping left-symmetric dialgebras
4.4 A linear basis of the free SLS-algebra
4.5 A criterion of speciality
5 Perm algebras under commutator and anti-commutator
5.1 On the commutator and anti-commutator
5.2 The results on the commutator and anti-commutator of perm algebra
5.3 Proof of theorems
5.3.1 Proof of Theorem
5.3.2 Proof of Theorem
5.3.3 Proof of Theorem
5.3.4 Proof of Theorem
5.3.5 Proof of Theorem
5.3.6 Proof of Theorem
5.4 The basis of universal enveloping perm algebras for metabelian Lie algebras
5.5 Proof of Theorem
6 Conclusion