Theta functions on noncommutative T4

@article{Kim2003ThetaFO,
  title={Theta functions on noncommutative T4},
  author={Hoil Kim and Chang-Yeong Lee},
  journal={Journal of Mathematical Physics},
  year={2003},
  volume={45},
  pages={461-474}
}
We construct the so-called theta vectors on noncommutative T4, which correspond to the theta functions on commutative tori with complex structures. Following the method of Dieng and Schwarz, we first construct holomorphic connections and then find the functions satisfying the holomorphic conditions, the theta vectors. The holomorphic structure in the noncommutative T4 case is given by a 2×2 complex matrix, and the consistency requires its off-diagonal elements to be the same. We also construct… Expand
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