In this paper we study associative unitary superalgebras with graded involution or superinvolution having polynomial growth of the codimension sequence. The first goal is to prove that, for this kind of algebras, the codimension sequence is a polynomial with rational coefficients. Then we shall construct several superalgebras with graded involution or superinvolution realizing the smallest and the largest value of the leading term of such a polynomial.

中文翻译：

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具有多项式增长的渐进对合或超对合的超代数

在本文中，我们研究具有渐进对合或具有超维对合维数序列增长的超对合的联合unit超代数。第一个目标是证明，对于这类代数，余维序列是一个有理系数的多项式。然后，我们将构造具有等级对合或超对合的几个超代数，以实现此类多项式的前导项的最小和最大值。