الملخص الإنجليزي
A Frobenius manifold is a geometric realization for a function F(t) satis_es a sys- tem of partial di_erential equation, (Witten-Dijkgraaf-Verlinde-Verlinde equation ), known as WDVV equations. This geometric structure is recognized in many _elds in mathematics such as topological _eld 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 _nd examples of polynomial Frobenius manifolds associated to regular Nilpotent element in Lie algebra sl(n;C):
