Partial and unified crossed products are weak crossed products
Abstract
In [J.M. Fern\'andez Vilaboa, R. Gonz\'alez Rodr\'iguez and A.B. Rodr\'iguez Raposo: Preunits and weak crossed products. J. of Pure Appl. Algebra 213, 2244-2261 (2009)] the notion of a weak crossed product of an algebra by an object, both living in a monoidal category was presented. Unified crossed products defined in [A. Agore, G. Militaru: Extending structures II: The quantum version. arXiv:1011.2174v3 (2011)] and partial crossed products defined in [M. Muniz S. Alves, E. Batista, M. Dokuchaev, A. Paques: Twisted partial actions of Hopf algebras. preprint (2011)] are crossed product structures defined for a Hopf algebra and another object. In this paper we prove that unified crossed products and partial crossed products are particular instances of weak crossed products.
Keywords
Cite
@article{arxiv.1110.6724,
title = {Partial and unified crossed products are weak crossed products},
author = {J. M. Fernández Vilaboa and R. González Rodríguez and A. B. Rodríguez Raposo},
journal= {arXiv preprint arXiv:1110.6724},
year = {2011}
}