二次余维增长与带有超逆运算的最小变分
Quadratic codimension growth and minimal varieties of unitary algebras with superinvolution
AI总结：
本文研究了带有超逆运算的单位代数的最小变种，通过二次余维增长的结构特征，揭示了其生成机制。
摘要：
设A是一个带有超逆运算*的结合代数，其中c_n^*(A)，n=1,2,…表示其*余维序列。已知该序列要么是多项式有界的，要么呈指数增长。在多项式情况下，PI理论中的一个中心问题是分类那些满足c_n^*(V)≈αn^k的变种V。本文的主要目标之一是分类带有超逆运算的单位代数的最小变种，其表现出二次余维增长。我们得到了所有具有二次余维增长的单位代数的结构特征，直至PI等价。作为结果，我们证明了任何具有二次余维增长的单位变种都由直接和生成最小变种的代数生成。
英文摘要：
Let $A$ be an associative algebra with a superinvolution $*$ over a field of characteristic zero, and let $c_n^*(A)$, $n = 1, 2, \ldots$, denote its sequence of $*$-codimensions. It is well known that this sequence is either polynomially bounded or grows exponentially. In the polynomial case, a central problem in PI-theory is the classification of varieties ${V}$ for which $c_n^*({V}) \approx αn^k$ for a given $k$. One of the main objectives of this paper is to classify minimal varieties of unitary algebras endowed with a superinvolution that exhibit quadratic codimension growth. We obtain a structural characterization, up to PI-equivalence, of all unitary algebras with quadratic codimension growth. As a consequence, we show that any unitary variety of quadratic codimension growth is generated by a direct sum of algebras generating minimal varieties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
