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Ali Fathi
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Quantization of of an elliptic curve can be done in different ways. In C^*-algebraic version, one can start with the C^*-algebra of continuous functions on ordinary torus and then by inserting a deformation parameter \theta into the product and obtain a deformed non-commutaive C^*-algebra of functions on the quantum torus.

My question is:

Is there any natural way for deformation quantization of closed Riemann surfaces with higher genus in the above sense?

Quantization of of an elliptic curve can be done in different ways. In C^*-algebraic version, one can start with the C^*-algebra of continuous functions on ordinary torus and then by inserting a deformation parameter \theta into the product and obtain a deformed non-commutaive C^*-algebra of functions on the quantum torus.

My question is:

Is there any natural way for deformation quantization of closed Riemann surfaces with higher genus in the above sense?

Quantization of of an elliptic curve can be done in different ways. In C^*-algebraic version, one can start with the C^*-algebra of continuous functions on ordinary torus and by inserting a deformation parameter \theta into the product obtain a deformed non-commutaive C^*-algebra of functions on the quantum torus.

My question is:

Is there any natural way for deformation quantization of closed Riemann surfaces with higher genus in the above sense?

Source Link
Ali Fathi
  • 309
  • 1
  • 6

Deformation quantization of a closed Riemann surface with genus >1

Quantization of of an elliptic curve can be done in different ways. In C^*-algebraic version, one can start with the C^*-algebra of continuous functions on ordinary torus and then by inserting a deformation parameter \theta into the product and obtain a deformed non-commutaive C^*-algebra of functions on the quantum torus.

My question is:

Is there any natural way for deformation quantization of closed Riemann surfaces with higher genus in the above sense?