From Projective Representations to Quasi-Quantum Groups

This is a contribution to the project of quiver approaches to quasi-quantum groups initiated in arXiv:0902.1620. We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations. This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras, or equivalently cofree pointed coalgebras, and helps to provide a projective representation-theoretic description of the gauge equivalence of graded pointed Majid algebras. We apply this machinery to construct some concrete examples and obtain a classification of finite-dimensional graded pointed Majid algebras with the set of group-likes equal to the cyclic group of order 2.