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REDUCED CROSSED PRODUCTS BY SEMIGROUPS OF AUTOMORPHISMS

Given a C-dynamical system (A, G, ) with a locally compact group G, two kinds of C-algebras are made from it, called the full C-crossed product and the reduced C-crossed product. In this paper, we extend the theory of the classical C-crossed product to the C-dynamical system (A, G, ) with a left-cancellative semigroup M with unit. We construct a new C-algebra A rM, the reduced crossed product of A by the semigroup M under the action and investigate some properties of A rM.