Bicrossproduct construction versus Weyl-Heisenberg algebra

TL;DR

This paper analyzes the Weyl-Heisenberg algebra using bicrossproduct construction, showing the possibility of a non-counital bialgebra structure and discussing implications for kappa-Poincare algebra.

Contribution

It introduces a non-counital bialgebra framework for the Weyl-Heisenberg algebra within bicrossproduct construction, which was not previously established.

Findings

Full bialgebra structure cannot be formed for Weyl-Heisenberg algebra

Non-counital bialgebra counterpart is possible

Remarks on bicrossproduct basis for kappa-Poincare algebra

Abstract

We are focused on detailed analysis of the Weyl-Heisenberg algebra in the framework of bicrossproduct construction. We argue that however it is not possible to introduce full bialgebra structure in this case, it is possible to introduce non-counital bialgebra counterpart of this construction. Some remarks concerning bicrossproduct basis for kappa-Poincare Hopf algebra are also presented.