A locally compact quantum group of triangular matrices

TL;DR

This paper constructs a new example of a locally compact quantum group by deforming the group of 2x2 upper triangular matrices with determinant 1, highlighting a non-trivial Haar measure deformation and describing its dual algebra.

Contribution

It introduces a one-parameter deformation of a classical matrix group into a locally compact quantum group with detailed dual algebra structure.

Findings

Haar measure is deformed non-trivially

Complete description of the dual *-algebra

Dual comultiplication characterized

Abstract

We construct a one parameter deformation of the group of $2\times 2$ upper triangular matrices with determinant 1 using the twisting construction. An interesting feature of this new example of a locally compact quantum group is that the Haar measure is deformed in a non-trivial way. Also, we give a complete description of the dual $\cs$-algebra and the dual comultiplication.