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Abstract
We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of the pentagon equation is extended to the non-unitary case. We establish the relation between Hopf-Galois algebras and solutions to the modified pentagon equation.
ACKNOWLEDGMENT
The work was started during my visit of Macquarie University (Sydney, Australia) and was completed in Max-Planck-Institut für Mathematik (Bonn, Germany). I would like to thank these institutions for hospitality and inspiring atmosphere. Special thanks to Prof. Ross Street who pointed out to me the references Citation[7], Citation[1] and explained his own work Citation[8].