6 papers
-Mock-Novikov Algebras: Structural Theory, Operad and Poisson-Type Constructions
Jie Ruan, Zafar Normatov
We introduce -mock-Novikov algebras as a parameter-dependent mock analogue of Novikov algebras. For , the commutator of a mock-Novikov algebra defines a Malcev algebra. Eve…
Mock-pre-Lie bialgebras
Shuai Hou, Zafar Normatov, Lina Song
In this paper, we systematically develop the theory of mock-pre-Lie bialgebras from multiple perspectives. We introduce the notion of a phase space of a mock-Lie algebra, and show…
Poisson -Lie algebras: constructions and the structure of solvable algebras
Xinru Cao, Zafar Normatov, Bakhrom Omirov
In this paper, we develop a construction of Poisson -Lie algebras that generalizes the Jacobian -Lie construction. Using the Grassmann--Plücker relations, we derive necessary…
Anti-associative dendriform algebras
Zafar Normatov
The general operadic approach to splitting algebraic operations was developed in \cite{BBGN}. By splitting the product in a given algebraic variety , notion of $\mathc…
Compatible anti-pre-Lie algebras
Zafar Normatov
In this paper, we introduce the notion of compatible anti-pre-Lie algebras and study relationship between them and the related structures such as anti--operators, comm…
Classification of four-dimensional anti-dendriform algebras whose associated associative algebra has the center of dimension one
Jobir Adashev, Artem Lopatin, Zafar Normatov +1
This article is devoted to the classification of anti-dendriform algebras that are associated with associativity. They are characterized as algebras with two operations whose sum i…