Representation Theory of the Algebra Generated By a Pair of Complex Structures

TL;DR

This paper classifies finite-dimensional indecomposable representations of an algebra generated by two complex structures, called iD-infinity, which relates to the infinite dihedral group.

Contribution

It provides a complete description of the indecomposable representations of the algebra generated by two complex structures, a novel classification in this context.

Findings

Classification of finite-dimensional indecomposable representations

Introduction of the algebra iD-infinity

Relation to the infinite dihedral group

Abstract

The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to those of the infinite dihedral group, we give the algebra the name iD-infinity.