A Kind Of Novikov Algebras And Triangle Functions

In this thesis ,we will establish the relation between Novikov algebras and other alge-bras,such as Lie algebra abelian algebra by the study of the Novikov algebra. Moreover,we will construct Novikov algebra over common functions. Some basic concepts of Novikov algebras will be recalled in the introduction.In section l,we introduce the relation between left symmetric algebra and Lie algebra,the relation between abelian algebra and Novikov algebras, in section 2,we will construct Novikov algebra over a kind of abelian associated algebras and it's derivations . In section 3, we construct Novikov algebra above over the linear space which generated by triangle functions.In the fourth section ,a Novikov algebra will be defined and be realized with a concrete example.The main results are as follow:THEOREM 1 Let (A,·) is a commutative algebra, d₀ is a derivation of A defined a bilinear operation "o" such that :then (A, d₀, o) is a Novikov algebra.THEOREM 2 Let A₁, A₂ are commutative and associative algebras over the field F, (?) :A₁,→ A₂ is a isomorphism of algebras and D₁ ∈ DerA₁. then1) D₂ = (?)D₁(?)^-1∈ DerA₂.2) (?): (A₁,D₁, o) → (A₂, D₂,o) is also a isomorphism of Novikov algebras. THEOREM 3 A₀ is the commutative associative algebra over R as above, D₀ isit's derivation satisfying (2.2). T is the commutative associative algebra over R as said in lemma 3.1 and lemma 3.2,then1) (?) :A₀ → T is a isomorphism as2)3) (?) : (A₀, a, o) → (T, (?)(a)d/dx, o) is a isomorphism of Novikov algebras. THEOREM 4 B₀ is a commutative associative algebra over R as above , D₀ isit's derivation satisfying (4.2).L is a commutative associative algebra over R as said in lemma 4.1 and lemma 3.2. f is a transform of ,then 1) (?):B₀→L such that is a isomorphism of commutative associative algebras.2)3) is a isomorphism of Novikov algebras.