L-R-smash products and L-R-twisted tensor products of algebras

TL;DR

This paper introduces the L-R-twisted tensor product, a unifying algebraic construction that generalizes existing products, and explores its properties, including invariance under twisting and iterability.

Contribution

It presents the L-R-twisted tensor product as a new generalization of L-R-smash and twisted tensor products, with foundational properties and iteration capabilities.

Findings

Proves invariance under twisting for the new product

Shows conditions for iterating L-R-twisted tensor products

Establishes the L-R-twisted tensor product as a unifying framework

Abstract

We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for instance we prove a result of the type "invariance under twisting" and we show that under certain circumstances L-R-twisted tensor products of algebras may be iterated.