We classify, up to PI-equivalence, the superalgebras over a field of characteristic zero whose sequence of codimensions is linearly bounded. As a consequence we determine the linear functions describing the graded codimensions of a superalgebra.

No abstract

We study the ∗-varieties of associative algebras with involution over a field of characteristic zero which\ud are generated by a finite-dimensional algebra. In this setting we give a list of algebras classifying all such\ud ∗-varieties whose sequence of ∗-codimensions is linearly bounded. Moreover, we exhibit a finite list of\ud algebras to be excluded from the ∗-varieties with such property. As a consequence, we find all possible\ud linearly bounded ∗-codimension sequences

No abstract

We study associative algebras with 1 endowed with an automorphism or antiautomor-\ud phism ' of order 2, i.e., superalgebras and algebras with involution. For any fixed k >=1,\ud we construct associative '-algebras whose '-codimension sequence is given asymptoti-\ud cally by a polynomial of degree k whose leading coefficient is the largest or smallest possi-\ud ble