Superálgebras unitárias com involução graduada ou superinvolução de crescimento polinomial

Abstract

If A is a superalgebra endowed with a graded involution or asuperinvolution, we say that A is a ψ-algebra. In this thesis we work with unitary ψ-algebras whose ψ-codimension sequence cψn(A) is polynomially bounded. Under this condition,we show that the sequence cψn(A) is decribed by a polynomial with rational coefficients. Moreover, we verify that the leading coefficient of the polynomial that describes the ψ-codimensions may assume only a finite number of possible values. Also, we provide examples of unitary ψ-algebras that realize the smallest and the biggest possible value of the leading coefficient. Lastly, we treatthe particular case related to unitary ψ-algebras of quadratic growth,showing examples of unitary ψ-algebras for each possible value of the leading coefficient of the polynomial describing cψn(A).