论文标题
弗罗贝尼乌斯代数几乎是弗罗贝尼乌斯的维度
Nearly Frobenius dimension on Frobenius algebras
论文作者
论文摘要
本文分为两个部分。在第一部分中，我们在一个字段$ \ mathbb {k} $上工作，并证明与Frobenius代数相关的Frobenius空间是由Frobenius coproduct生成的。特别是，我们证明了Frobenius维度与代数的维度一致。在第二部分中，我们与可交换的环$ k $一起工作。在这种情况下，我们介绍了几乎弗罗贝尼乌斯代数的概念，并构建了杨巴克斯特方程的解决方案，从弗罗贝尼乌斯空间中的元素开始。此外，我们提供了几乎弗罗贝尼乌斯代数的等效特征列表。
This article is divided into two parts. In the first part we work over a field $\mathbb{k}$ and prove that the Frobenius space associated to a Frobenius algebra is generated as left A-module by the Frobenius coproduct. In particular, we prove that the Frobenius dimension coincides with the dimension of the algebra. In the second part we work with a commutative ring $k$. We introduce the concept of nearly Frobenius algebras in this context and construct solutions of the Yang-Baxter equation starting from elements in the Frobenius space. Also, we give a list of equivalent characterizations of nearly Frobenius algebras.
