2003/03/31 by Hoil Kim, Chang-Yeong Lee, Chang‐Yeong Lee · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Black Holes and Theoretical Physics #Commutative property #Computer science #Consistency (knowledge bases) #Construct (python library) #Diagonal #Discrete mathematics #Geometry #Holomorphic function #Identity theorem #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Pure mathematics #Tensor (intrinsic definition) #Tensor product #hep-th #math.QA
paper · pdf · doi:10.1063/1.1629778
published as J.Math.Phys. 45 (2004) 461-474 · 17 pages, LaTeX, references added, typos corrected, version to appear in J. Math. Phys
arxiv created 2003/10/06 · openalex publication_date 2003/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 the tensor product of these functions satisfying the consistency requirement.