Representation theory of C-algebras for a higher order class of spheres and tori

TL;DR

This paper develops a new class of C-algebras associated with higher order surfaces, analyzing their representation theory through dynamical systems, and introduces Henon algebras linked to generalized Henon maps with diverse irreducible representations.

Contribution

It constructs C-algebras for complex surfaces and explores their representations via graph and dynamical systems, including the novel Henon algebras.

Findings

Representation theory relates to loop and string representations.

Existence of irreducible representations of all dimensions for certain algebras.

Introduction of Henon algebras connected to generalized Henon maps.

Abstract

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and ``string'' representations, which are closely related to the dynamics of an iterated map in the plane. As a particular class of algebras we introduce the ``Henon algebras'', for which the dynamical map is a generalized Henon map, and give an example where irreducible representations of all dimensions exist.