Inductive Algebras for Finite Heisenberg Groups

TL;DR

This paper characterizes maximal abelian sub-algebras in matrix algebras normalized by finite Heisenberg group representations, providing a classification-based construction of examples.

Contribution

It offers a new characterization of maximal abelian sub-algebras normalized by finite Heisenberg groups and constructs examples via classification results.

Findings

Characterization of maximal abelian sub-algebras in matrix algebras

Construction of examples using classification of finite Heisenberg groups

Insight into the structure of algebras normalized by Heisenberg group representations

Abstract

A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite Heisenberg groups.