Iterated weak crossed products

TL;DR

This paper develops a method to iteratively construct new weak crossed products with a common monoid, expanding the algebraic framework for such products.

Contribution

It provides sufficient conditions for combining weak crossed products iteratively, advancing the understanding of their algebraic structure.

Findings

Established conditions for iterating weak crossed products

Constructed new weak crossed products from existing ones

Enhanced the algebraic toolkit for weak crossed product analysis

Abstract

In this paper we show how iterate weak crossed products with common monoid. More concretely, if $(A\otimes V, \mu_{A\otimes V})$ and $(A\otimes W, \mu_{A\otimes W})$ are weak crossed products, we find sufficient conditions to obtain a new weak crossed product $(A\otimes V\otimes W, \mu_{A\otimes V\otimes W})$