2005/08/22 by Kadison, Lars
#13B05 #16W30 #20L05 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.math/0508411
A pseudo-Galois extension is shown to be a depth two extension. Studying its left bialgebroid, we construct an enveloping Hopf algebroid for the semi-direct product of groups, or more generally involutive Hopf algebras, and their module algebras. It is a type of cofibered sum of two inclusions of the Hopf algebra into the semi-direct product and its derived right crossed product. Van Oystaeyen and Panaite observe that this Hopf algebroid is non-trivially isomorphic to a Connes-Moscovici Hopf algebroid, which raises interesting comparative questions.