Theta-functions on noncommutative tori
量子代数
2007-05-23 v1 高能物理 - 理论
摘要
Ordinary theta-functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta-functions as holomorphic elements of projective modules over noncommutative tori (theta-vectors). The theory of these new objects is not only more general, but also much simpler than the theory of ordinary theta-functions. It seems that the theory of theta-vectors should be closely related to Manin's theory of quantized theta-functions, but we don't analyze this relation.
引用
@article{arxiv.math/0107186,
title = {Theta-functions on noncommutative tori},
author = {Albert Schwarz},
journal= {arXiv preprint arXiv:math/0107186},
year = {2007}
}