Quantum algebras with supersymmetries

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The project aims to make fundamental advances in the theory of quantum algebras. It will develop explicit structure and representation theory of major classes of quantum algebras which are of great importance to quantum field theory and integrable models with supersymmetries. The intended outcomes include a solution of the outstanding classification problem for representations of quantum algebras with supersymmetries, which has remained open for the last two decades. It will involve newly-developed methods within the theory of quantum groups, and both the methods and classification will bring new mathematical instruments for the advance of supesymmetric conformal field theory and soliton spin chain models.