Theta functions on noncommutative T4 | Zendy

Hoil Kim | Zendy; ChangYeong Lee | Zendy

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Theta functions on noncommutative T4

Author(s) -

Hoil Kim,

ChangYeong Lee

Publication year - 2003

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.1629778

Subject(s) - noncommutative geometry , holomorphic function , mathematics , pure mathematics , tensor product , identity theorem , commutative property , diagonal , construct (python library) , noncommutative quantum field theory , tensor (intrinsic definition) , algebra over a field , consistency (knowledge bases) , discrete mathematics , geometry , computer science , programming language

We construct the so-called theta vectors on noncommutative T^4, whichcorrespond to the theta functions on commutative tori with complex structures.Following the method of Dieng and Schwarz, we first construct holomorphicconnections and then find the functions satisfying the holomorphic conditions,the theta vectors. The holomorphic structure in the noncommutative T^4 case isgiven by a 2x2 complex matrix, and the consistency requires its off-diagonalelements to be the same. We also construct the tensor product of thesefunctions satisfying the consistency requirement.Comment: 17 pages, LaTeX, references added, typos corrected, version to appear in J. Math. Phy

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