Abstract
Abstract 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.].
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