Equivalent Crossed Products and Cross Product Bialgebras

Abstract

In a previous article we proved a result of the type “invariance under twisting” for Brzeziński's crossed products. In this article we prove a converse of this result, obtaining thus a characterization of what we call equivalent crossed products. As an application, we characterize cross product bialgebras (in the sense of Bespalov and Drabant) that are equivalent (in a certain sense) to a given cross product bialgebra in which one of the factors is a bialgebra and whose coalgebra structure is a tensor product coalgebra.

Key Words:

• Crossed product
• Cross product bialgebra
• Invariance under twisting

2010 Mathematics Subject Classification:

• 16S35
• 16S40
• 16T10

ACKNOWLEDGMENT

This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0635, contract nr. 253/5.10.2011.

Dedicated to Fred Van Oystaeyen, on the occasion of his 65th birthday.

Notes

Communicated by M. Cohen.