Color involutions on upper triangular matrices and almost polynomial growth of ⁎-varieties

Let G be a finite abelian group and A be a G -graded algebra endowed with a color involution ⁎. We first classify all color involutions on the algebra of n×n upper triangular matrices. We then provide a classification of the ⁎-varieties of almost polynomial growth generated by finitely generated G -graded ⁎-algebras. As a consequence, we prove that the ⁎-codimension sequence is either polynomially bounded or exhibits exponential growth.