Superalgebras with graded involution: classifying minimal varieties of quadratic growth

Abstract Let V be a variety of superalgebras with graded involution and let c n gri ( V ) be its sequence of ⁎-graded codimensions. We say that V has polynomial growth n k if asymptotically c n gri ( V ) ≈ a n k , for some a ≠ 0 . Furthermore, V is minimal of polynomial growth n k if c n gri ( V ) grows as n k and any proper subvariety of V has polynomial growth n t , with t k . In this paper, we classify superalgebras with graded involution generating minimal varieties of quadratic growth.