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Group-Like algebras and Hadamard matrices

Mariana Haim
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Abstract

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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Mariana Haim. 2006-02-10. Group-Like algebras and Hadamard matrices. https://arxiv.org/abs/math/0602224

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