In this paper we prove that if A is any algebra with involution * satisfying a non-trivial polynomial identity, then its sequence of *-codimensions is eventually non-decreasing. Furthermore, by making use of the *-exponent we reconstruct the only two *-algebras, up to T *-equivalence, generating varieties of almost polynomial growth. As a third result we characterize the varieties of algebras with involution whose exponential growth is bounded by 2.

中文翻译：

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星代数的余维和低指数增长

在本文中，我们证明如果 A 是任何具有对合 * 满足非平凡多项式恒等式的代数，那么它的 *-codimensions 序列最终是非递减的。此外，通过使用 *-指数，我们重建了仅有的两个 *-代数，直到 T *-等价，生成几乎多项式增长的变体。作为第三个结果，我们描述了指数增长以 2 为界的对合代数的变体。