Group-like algebras and Hadamard matrices
Group-like algebras and Hadamard matrices
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DOI：
10.1016/j.jalgebra.2006.06.005
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发表时间：
2006-02
影响因子：
0.9
通讯作者：
M. Haim
中科院分区：
文献类型：
--
作者：
M. Haim
本文给出了S_（？）id=id_（？）S=u_ε的类群代数族的方阵描述。在S=id和k <$R的情况下，这种转换将我们带到Hadamard矩阵，特别是满足S <$id=id <$S=uε的双弗罗贝纽斯代数的例子，并且不是Hopf代数。最后，我们将有限维Hopf代数的可分性和余可分性的一些已知结果推广到这类特殊的双Frobenius代数上，给出了这类双Frobenius代数的Maschke定理的一个版本.
We give a description in terms of square matrices of the family of group-like algebras with S∗id=id∗S=uε. In the case that S=id and k⊆R, this translation take us to Hadamard matrices and, particularly, to examples of bi-Frobenius algebras satisfying S∗id=id∗S=uε and that are not Hopf algebras. Finally, we generalize some known results on separability and coseparability valid for finite-dimensional Hopf algebras to this special class of bi-Frobenius algebras with S∗id=id∗S=uε, presenting a version of Maschke's theorem for this family.