Theta functions on Noncommutative T^4

Abstract

We construct the so-called theta vectors on noncommutative T^4, 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 T^4 case is given by a 2x2 complex matrix, and the consistency requires its off-diagonal elements to be the same. We also construct the tensor product of these functions satisfying the consistency requirement.

arXiv comment17 pages, LaTeX, references added, typos corrected, version to appear in J. Math. Phys

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Cited by in corpus (6)

• Theta Vectors and Quantum Theta Functions
• Categories of holomorphic line bundles on higher dimensional noncommutative complex tori
• Noncommutative Riemann Conditions
• Quantum Thetas on Noncommutative T^d with General Embeddings
• Quantum Thetas on Noncommutative T^4 from Embeddings into Lattice
• Symmetry of Quantum Torus with Crossed Product Algebra