L-R-crossed products

TL;DR

This paper introduces L-R-crossed products, a new associative algebra construction on tensor products that generalizes several existing algebraic structures like Brzezinski crossed products and L-R-smash products.

Contribution

It defines the L-R-crossed product and shows how it encompasses various known algebraic constructions as special cases.

Findings

Defines the L-R-crossed product structure.

Demonstrates the generality by recovering known constructions.

Provides axioms ensuring associativity.

Abstract

Given an associative algebra H, a linear space U and some linear maps J, T, \gamma , \eta satisfying some axioms, we define an associative algebra structure on U\otimes H, called an L-R-crossed product. This contains as particular cases some previous constructions, such as the (iterated) Brzezinski crossed product and the L-R-smash product over quasi-bialgebras.