Inductive algebras for the motion group of the plane

TL;DR

This paper explores the structure of inductive algebras associated with the motion group of the plane, revealing that each irreducible representation has a unique maximal self-adjoint inductive algebra.

Contribution

It establishes the existence and uniqueness of maximal inductive algebras for all irreducible representations of the motion group of the plane.

Findings

Each irreducible representation has a unique maximal inductive algebra.

These algebras are self-adjoint.

The result characterizes the algebraic structure of the motion group representations.

Abstract

Each irreducible representation of the motion group of the plane has a unique maximal inductive algebra, and it is self adjoint.