Duality of algebras with an involution and generalized shift operators

A survey is given of works in which L. S. Pontryagin's duality principle is extended to various classes of, generally speaking, noncommutative, generalized shift operators. The discussion is carried out with the use of the theory of Kac algebras and its generalizations. A number of problems are formulated.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 24, pp. 165–205, 1986.