Abstract In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: D 2 , the algebra of 2 × 2 diagonal matrices and C 2 , the algebra of 2 × 2 matrices generated by e 11 + e 22 and e 12 . We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential.

中文翻译：

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跟踪恒等式和几乎多项式增长

摘要 在本文中，我们研究了具有迹的代数及其在特征为 0 的域上的迹多项式恒等式。我们考虑两个交换矩阵代数：D 2 ，2 × 2 对角矩阵的代数和 C 2 ，2 × 2 矩阵的代数由 e 11 + e 22 和 e 12 生成。我们描述了这些代数上所有可能的迹，并研究了相应的迹余维。此外，我们用有限维代数生成的多项式增长的痕迹来表征变体。因此，我们看到具有迹的品种的增长要么是多项式的，要么是指数的。