类群代数与Hadamard矩阵

摘要：

给出了具有$S*id=id*S=uε$的类群代数族的方阵描述。在$S=id$和$char\Bbbk$不是2并且不划分代数的维数的情况下，这种转换将我们带到Hadamard矩阵，特别是满足$S*id=id*S=uε$并且不是霍普夫代数的biFrobenius代数的例子。最后，我们利用$S*id=id*S=uε$将有限维霍普夫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，给出了该类双Frobenius代数的Maschke定理的一个版本.

英文摘要：

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 $char\Bbbk$ is not 2 and does not divide the dimension of the algebra, this translation take us to Hadamard matrices and, particularly, to examples of biFrobenius 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 biFrobenius algebras with $S*id=id*S=uε$, presenting a version of Maschke's theorem for this family.

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