Fuzzy Riemann Surfaces

Abstract

We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras.

References in corpus (4)

• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• The Dynamics of Relativistic Membranes I: Reduction to 2-dimensional Fluid Dynamics
• Membrane topology and matrix regularization
• All Higher Genus BPS Membranes in the Plane Wave Background

Cited by in corpus (20)

• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
• Matrix embeddings on flat $R^3$ and the geometry of membranes
• Matrix Geometry and Coherent States
• Non-Compact Hopf Maps and Fuzzy Ultra-Hyperboloids
• Emergent Geometry from Quantized Spacetime
• Information metric, Berry connection and Berezin-Toeplitz quantization for matrix geometry
• The world as quantized minimal surfaces
• Kähler structure in the commutative limit of matrix geometry
• The matrix regularization for Riemann surfaces with magnetic fluxes
• Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects
• Nahm equations in supersymmetric mechanics
• Noncommutative Spherically Symmetric Spaces
• Category of Quantizations and Inverse Problem
• Deformed Noncommutative Tori
• Categorical Perspective on Quantization of Poisson Algebra
• Low dimensional matrix representations for noncommutative surfaces of arbitrary genus
• Unusual Thermodynamics on the Fuzzy 2-Sphere
• Beyond fuzzy spheres
• Deformation of Matrix Geometry via Landau Level Evolution