On self-adjoint representations of the sklyanin algebras

Self-adjoint representations in Hilbert space of a family of quadratic algebras constructed by E. K. Sklyanin are studied. Complete sets of classes of unitary equivalence of irreducible representations are obtained for algebras that correspond to second-order points of elliptic curves.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 11, pp. 1567–1574, November, 1991.