*-Variedades minimais e supervariedades minimais de crescimento polinomial

Abstract

By a ϕ-variety V we mean a supervariety or a ∗-variety generated by an associative algebra over a field F of characteristic zero. In this case, we can consider its sequence of ϕ-codimensions cϕ n(V). We say that V is minimal of polynomial growth nk if cϕ n(V) grows like nk,k > 0, but cϕ n(U) grows like nt with t < k, for any proper ϕ-subvariety U of V. In this thesis, we deal with minimal ϕ-varieties generated by unitary algebras and prove that for k ≤ 2 there are only a finite number of them. We also explicit a list of finite dimensional algebras generating such minimal ϕ-varieties. For k ≥ 3, we show that the number of minimal ϕ-varieties can be infinity and we classify all minimal ϕ-varieties of polynomial growth nk by providing a method for the construction of their ϕ-ideals.