Associativity of Some Skew Semigroup Rings
Abstract
Given a partial action α of a discrete group G on an associative algebra A. The notion of skew group ring A×αG, corresponding to α is introduced by M. Dokuchaev and R. Exel in [1] where the associativity of A×αG is proved for a semiprime algebra A. We generalize this idea to an action of a unital inverse semigroup S on an arbitrary C* -algebra A. Also, we introduce the notion of skew semigroup ring A×βS and we prove its associativity without using approximate identity.
Keywords
C* -algebra, partial action, partial automorphism, skew group ring