English abstract
A Frobenius manifold is a geometric realization for a function F(t) satisfies a sys tem of partial differential equation, (Witten-Dijkgraaf-Verlinde-Verlinde equation ), known as WDVV equations.
This geometric structure is recognized in many fields in mathematics such as topological field theory, invariant theory, quantum cohomology, integrable systems and singularity theory Frobenius manifold is called algebraic if the function F(t) is algebraic function. Examples of algebraic Frobenius manifolds can be obtained from the dispersionless limit of classical W-algebras associated to distinguished Nilpotent elements of semisimple type in simple Lie algebras. In this thesis, we apply the same procedure to find examples of polynomial Frobenius manifolds associated to regular Nilpotent element in Lie algebra slan, C).
