An elementary Green imprimitivity theorem for inverse semigroups

2014/05/07 by Burgstaller, Bernhard
#20M18 #46L08 #46L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1405.1619

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 \rtimes H is Morita equivalent to a certain crossed product B \rtimes G.

Related

• Strong Morita Equivalence of Inverse Semigroups
• Crossed Products by Partial Actions of Inverse Semigroups
• Characterizations of Morita equivalent inverse semigroups
• Partial Crossed Product of a group G vs Crossed Product of S(G)
• Classes of semigroups modulo Green's relation H