In this article,we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras,bicommutative algebras,and assosymmetric algebras.More precisely,we first study the properties of t...In this article,we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras,bicommutative algebras,and assosymmetric algebras.More precisely,we first study the properties of the lower central chains for Novikov algebras and bicommutative algebras.Then we show that for every Lie nilpotent Novikov algebra or Lie nilpotent bicommutative algebra A,the ideal of A generated by the set{ab−ba|a,b∈A}is nilpotent.Finally,we study properties of the lower central chains for assosymmetric algebras,study the products of commutator ideals of assosymmetric algebras and show that the products of commutator ideals have a similar property as that for associative algebras.展开更多
In the paper we will give a complete classification of finite-dimemsional simple Novikov algebras over an algebraically closed field with prime characteristic p>2.
This paper gives some sufficient conditions for determining the simplicity of infinite di-mensional Novikov algebras of characteristic 0, and also constructs a class of simple Novikovalgebras by extending the base fie...This paper gives some sufficient conditions for determining the simplicity of infinite di-mensional Novikov algebras of characteristic 0, and also constructs a class of simple Novikovalgebras by extending the base field. At last, the deformation theory of Novikov algebras isintroduced.展开更多
In this paper we show that an A-module is a direct sum of a trivial module and a nosingular module,and we also give the structure of nonsingular module over infinite dimensional simple Novikov algebras of types (Ⅱ) a...In this paper we show that an A-module is a direct sum of a trivial module and a nosingular module,and we also give the structure of nonsingular module over infinite dimensional simple Novikov algebras of types (Ⅱ) and (Ⅲ) over a field F of Characteristic 0.展开更多
In this paper,we construct two kinds of infinite-dimensional Novikov algebras and give their realizations,respectively.As an application,we describe their sub-adjacent Lie algebras and characterize some of their prope...In this paper,we construct two kinds of infinite-dimensional Novikov algebras and give their realizations,respectively.As an application,we describe their sub-adjacent Lie algebras and characterize some of their properties.展开更多
基金supported by FCT(Grant No.UIDB/00212/2020)FCT(Grant No.UIDP/00212/2020)+5 种基金supported by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan(Grant No.AP14869221)by“Tayelsizdik urpaqtary”MISD RKpartially supported by the Simons Foundation Targeted Grant for the Institute of Mathematics–VAST(Grant No.558672)by the Vietnam Institute for Advanced Study in Mathematics(VIASM)supported by the NNSF of China(Grant No.12101248)by the China Postdoctoral Science Foundation(Grant No.2021M691099)。
文摘In this article,we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras,bicommutative algebras,and assosymmetric algebras.More precisely,we first study the properties of the lower central chains for Novikov algebras and bicommutative algebras.Then we show that for every Lie nilpotent Novikov algebra or Lie nilpotent bicommutative algebra A,the ideal of A generated by the set{ab−ba|a,b∈A}is nilpotent.Finally,we study properties of the lower central chains for assosymmetric algebras,study the products of commutator ideals of assosymmetric algebras and show that the products of commutator ideals have a similar property as that for associative algebras.
文摘In the paper we will give a complete classification of finite-dimemsional simple Novikov algebras over an algebraically closed field with prime characteristic p>2.
文摘This paper gives some sufficient conditions for determining the simplicity of infinite di-mensional Novikov algebras of characteristic 0, and also constructs a class of simple Novikovalgebras by extending the base field. At last, the deformation theory of Novikov algebras isintroduced.
文摘In this paper we show that an A-module is a direct sum of a trivial module and a nosingular module,and we also give the structure of nonsingular module over infinite dimensional simple Novikov algebras of types (Ⅱ) and (Ⅲ) over a field F of Characteristic 0.
文摘In this paper,we construct two kinds of infinite-dimensional Novikov algebras and give their realizations,respectively.As an application,we describe their sub-adjacent Lie algebras and characterize some of their properties.
