论文标题
痕量身份和几乎多项式增长
Trace identities and almost polynomial growth
论文作者
论文摘要
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 $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $ e_ {12} $。我们描述了这些代数上的所有可能痕迹，并研究了相应的痕量编辑。此外，我们以有限维代数产生的多项式生长的痕迹来表征这些品种。结果，我们看到痕迹的多样性的生长是多项式或指数。
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 $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ 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.
