Types Novikov Algebra And Its Implementation

Novikov algebras is a kind of algebras that contact with Lie algebras and it isgenerated by the study of Hamiltonian operators. In1985, the definition of Novikovalgebras was given by Balinskii and Novikov, final it was named by Osborn.A Novikov algebras is a vector space over a field F with a bilinear product(x, y)â†'xy satisfying(x1,x2,x3)=(x2,x1,x3)and (x1x2)x3=(x1x3)x2for x1, x2, x3∈A, where(x1,x2,x3)=(x1x2)x3-x1(x2+x3)Novikov algebras is a left-symmetric algebras which only satisfy equation the firstequation.For a Novikov algebras, the left multiplication operators are symmetric andthe right multiplication operators are commutative, Novikov algebras is connec-tion with hydrodynamic. Because of the mathematics and physics have great linkwith Novikov algebras in the many branches, we study Novikov algebras that al-lows us to use mathematical knowledge to solve physical problems and promote thedevelopment of mathematics and physics, so the Novikov algebras has theoreticalsignificance and application value on researched and it solve the practical problemshave a guiding role.In this paper, we construct several kinds of infinite-dimensional Novikov alge-bras and give their realizations. In the first chapter, we introduces Novikov algebrasand the current situation of the development of Novikov algebras. The second, thethird and the final chapter we give their realizations by polynomials, combinatorialtriangle functions and exponential functions, Euler's functions. For the realizationof the Novikov algebras, we use specific function and specific model to study abstractNovikov algebras, It has a application value and practical significance.