An elementary Green imprimitivity theorem for inverse semigroups

Abstract

A Morita equivalence similar to that found by Green for crossed products by groups will be established for crossed products by inverse semigroups. More precisely, let G be an inverse semigroup, H a finite sub-inverse semigroup of G and A a G-algebra or a H-algebra. Then the crossed product A ⋊ H is Morita equivalent to a certain crossed product B ⋊ G.1991 Mathematics Subject Classification. 46L55, 20M18, 46L08.