Algebra of Noncommutative Riemann Surfaces

Abstract

We examine several algebraic properties of the noncommutive $z$-plane and Riemann surfaces. The starting point of our investigation is a two-dimensional noncommutative field theory, and the framework of the theory will be converted into that of a complex coordinate system. The basis of noncommutative complex analysis is obtained thoroughly, and the considerations on functional analysis are also given before performing the examination of the conformal mapping and the Teichmüller theory. (Keywords; Complex Analysis, Riemann Surfaces and Teichmüller Space, Functional Analysis, Deformation Quantization, Non-Commutative Geometry, Quantum Groups)

25 pages

References in corpus (8)

• Deformation quantization of Poisson manifolds, I
• Noncommutative Field Theory
• Operads and Motives in Deformation Quantization
• A Short Survey of Noncommutative Geometry
• Supersymmetric quantum theory and non-commutative geometry
• Quantum fields and motives
• Path Integral for Space-time Noncommutative Field Theory
• Deformation Quantization and Quaternions

Cited by in corpus (4)

• Dynamical Mass Generations and Collective Excitations in the (Supersymmetric-)Nambu$-$Jona-Lasinio Model and a Gauge Theory with Left-Right-Asymmetric Majorana Mass Terms
• Moyal-Weyl Star-products as Quasiconformal Mappings
• Deformation Quantization and Quaternions
• Noncommutative Deformations of Locally Symmetric Kähler manifolds