Representations of quadratic ∗-algebras by bounded and unbounded operators

This survey is based on the works of Kiev mathematicians and other works in the field of structure theory of collections of bounded and unbounded self-adjoint operators that satisfy algebraic relations. The families of (unbounded) operators that are connected by algebraic relations arise in the theory of representations of quantum groups [27, 30, 36, 37, etc.], quantum homogeneous spaces [29, 30, etc.], and Sklyanin algebras [33, etc.].