TL;DR
This paper introduces a mirror version of Brzezinski's crossed product and demonstrates how these can be iterated to form complex algebra structures, including twisted tensor products and smash products.
Contribution
It defines a new mirror crossed product and proves conditions for its iteration with existing crossed products, expanding algebra construction techniques.
Findings
Established a mirror version of Brzezinski's crossed product.
Proved conditions for iterating crossed products to form new algebra structures.
Connected the construction to known algebraic products like twisted tensor and smash products.
Abstract
We define a "mirror version" of Brzezinski's crossed product and we prove that, under certain circumstances, a Brzezinski crossed product D\otimes_{R, \sigma}V and a mirror version W\bar{\otimes}_{P, \nu}D may be iterated, obtaining an algebra structure on W\otimes D\otimes V. Particular cases of this construction are the iterated twisted tensor product of algebras and the quasi-Hopf two-sided smash product.
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