Two-sided crossed products

TL;DR

This paper introduces the two-sided crossed product, an associative algebra structure on the tensor product of two algebras and a linear space, generalizing iterated twisted tensor products and crossed products over quasi-bialgebras.

Contribution

It defines a new algebraic construction called the two-sided crossed product, expanding the framework of tensor products and crossed products in algebra.

Findings

Defines the two-sided crossed product structure.

Shows it generalizes iterated twisted tensor products.

Connects to crossed products over quasi-bialgebras.

Abstract

Given two associative algebras A, C and a linear space V together with some linear maps R_1, R_2, R_3, E satisfying some conditions, we define an associative algebra structure on A\otimes V\otimes C called a two-sided crossed product. Particular cases of this construction are the iterated twisted tensor product of algebras and the two-sided crossed product over a quasi-bialgebra.