On possible values of the interior angle between intermediate subalgebras

TL;DR

This paper investigates the range of possible interior angles between intermediate subalgebras in certain C*-algebra inclusions, providing explicit calculations for crossed product subalgebras under group actions.

Contribution

It demonstrates that all angles in [0, π/2] are attainable and computes these angles for crossed product subalgebras under group actions.

Findings

All angles in [0, π/2] can be realized as interior angles.

Explicit formulas for angles between crossed product subalgebras.

Applicable to inclusions of simple unital C*-algebras and group actions.

Abstract

We show that all values in the interval $[0,\frac{\pi}{2}]$ can be attained as the interior angle between intermediate subalgebras (as introduced in [3]) of a certain inclusion of simple unital C*-algebras. We also calculate the interior angle between intermediate crossed product subalgebras of any inclusion of crossed product algebras corresponding to any action of a countable discrete group and its subgroups on a unital C*-algebra.