Iterated crossed products. (Q2874700)

\textit{T. Brzeziński} [Commun. Algebra 25, No. 11, 3551-3575 (1997; Zbl 0887.16026)] introduced a very general notion of crossed product, \(A\otimes_{R,\sigma}V\), of an associative algebra and a vector space \(V\) with a distinguished element \(1_V\) and two maps \(\sigma\colon V\otimes V\to A\otimes V\) and \(R\colon V\otimes A\to A\otimes V\).NEWLINENEWLINE In this paper, the author constructs a ``mirror'' version \(W\overline\otimes_{P,\nu}B\) and shows that under some conditions it can be iterated and an iterated crossed product is obtained. Examples of this construction are the iterated twisted tensor product [\textit{P. Jara Martínez} et al., Int. J. Math. 19, No. 9, 1053-1101 (2008; Zbl 1167.16023)], quasi-Hopf two-sided smash product [\textit{D. Bulacu} et al., Commun. Math. Phys. 266, No. 2, 355-399 (2006; Zbl 1159.16027)] and a bialgebra introduced by \textit{Y. Sommerhäuser} [New York J. Math. 2, 35-58 (1996; Zbl 0879.16028)].