Hopf Algebras and Biunitary Matrices

Hopf ∗-algebras Associated to Biunitary Matrices

Actually to any spin model one can associate a vertex model (this is clear from V. Jones’ initial interpretation – in terms of statistical mechanics – of these objects) and the construction of Hopf algebras from complex Hadamard matrices is a particular case of the construction of Hopf algebras from biunitary matrices. This is done in section 5 in [3]. The construction of Hopf algebras from biu...

Biunitary constructions in quantum information

We present an infinite number of constructions involving unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on biunitary connections, algebraic objects which play a central role in the theory of planar algebras. They have an attractive graphical calculus which allows simple correctness proofs ...

On the Coderivations of Some Hopf Algebras

NOTES ON REGULAR MULTIPLIER HOPF ALGEBRAS

In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition

Gorenstein global dimensions for Hopf algebra actions

Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra‎. ‎In this paper‎, ‎we investigate Gorenstein global dimensions for Hopf‎ ‎algebras and twisted smash product algebras $Astar H$‎. ‎Results from‎ ‎the literature are generalized‎.