On a class of quasi-Frobenius algebras
On a class of quasi-Frobenius algebras
复制标题
关于一类拟 Frobenius 代数
DOI：
10.1016/j.jpaa.2021.106992
复制
发表时间：
2021
影响因子：
0.8
通讯作者：
L. Nastasescu
中科院分区：
文献类型：
--
作者：
S. Dascalescu;C. Nastasescu;L. Nastasescu
我们从两个矩阵余代数E和F出发，通过邻接两个元素族，以矩阵形式的方式，构造了一类有限维余代数，它们关于E和F的行为类似于某种斜本原.证明了所得到的余代数是拟余Frobenius代数，但它们是余Frobenius代数的前提是E和F具有相同的尺寸.利用对偶代数，我们得到了一大类非Frobenius的拟Frobenius代数的例子。
We construct in a natural way a class of finite dimensional coalgebras by starting with two matrix coalgebras E and F, and then by adjoining two families of elements which in a matrix-formal way behave like some kind of skew-primitives with respect to E and F. We show that the obtained coalgebras are quasi-co-Frobenius, but they are co-Frobenius only when E and F have the same size. By taking the dual algebras, we obtain a large class of examples of quasi-Frobenius algebras which are not Frobenius.