On the tensor product of two oriented quantum algebras

TL;DR

This paper explores how to construct oriented quantum algebra structures on tensor products of two OQAs using Chen's weak R-matrix, providing new insights and different results from previous studies.

Contribution

It introduces a method to define OQA structures on tensor products using Chen's weak R-matrix, including new cases not covered by earlier work.

Findings

OQA structures on tensor products are established

New OQA structures differ from Radford's results

Special case of OQA with itself is analyzed

Abstract

In this paper, we give the oriented quantum algebra (abbr. OQA) structures on the tensor product of two different OQAs by using Chen's weak $\mathfrak{R}$-matrix in [J. Algebra 204(1998):504-531]. As a special case, the OQA structures on the tensor product of an OQA with itself are provided, which are different from Radford's results in [J. Knot Theory Ramifications 16(2007):929-957].