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

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

2007-11-19

arxiv.org/abs/0711.2943v1

Physics

Mathematical Physics

14 pages

Scientific paper

10.1063/1.2913523

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.

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