# Algebra of Noncommutative Riemann Surfaces

@article{Ohsaku2006AlgebraON, title={Algebra of Noncommutative Riemann Surfaces}, author={Tadafumi Ohsaku}, journal={arXiv: Mathematical Physics}, year={2006} }

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 Teichmuller theory…

## 4 Citations

### Moyal-Weyl Star-products as Quasiconformal Mappings

- Mathematics
- 2006

The relation between the Moyal-Weyl deformation quantization and quasiconformal mappings of Riemann surfaces of complex analysis are shown by several examples.

### Deformation Quantization and Quaternions

- Physics
- 2006

The deformation quantization of Moyal-Weyl star product of functions of quaternions is investigated.

### Dynamical Mass Generations and Collective Excitations in the (Supersymmetric-)Nambu-Jona-Lasinio Model and a Gauge Theory with Left-Right-Asymmetric Majorana Mass Terms

- Physics
- 2008

The structure of effective potential surface of the Nambu$-$Jona-Lasinio (NJL) model with right-left asymmetric Majorana mass terms (corresponds to the single-flavor type-II seesaw situation of…

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