Hopf-Frobenius Algebras and a Simpler Drinfeld Double

@article{Collins2020HopfFrobeniusAA,
  title={Hopf-Frobenius Algebras and a Simpler Drinfeld Double},
  author={Joseph Collins and Ross Duncan},
  journal={Electronic Proceedings in Theoretical Computer Science},
  year={2020}
}
The ZX-calculus and related theories are based on so-called interacting Frobenius algebras, where a pair of $†$-special commutative Frobenius algebras jointly form a pair of Hopf algebras. In this setting we introduce a generalisation of this structure, Hopf-Frobenius algebras, starting from a single Hopf algebra which is not necessarily commutative or cocommutative. We provide the necessary and sufficient condition for a Hopf algebra to be a Hopf-Frobenius algebra, and show that every Hopf… 

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