Star product formula of theta functions

Abstract

As a noncommutative generalization of the addition formula of theta functions, we construct a class of theta functions which are closed with respect to the Moyal star product of a fixed noncommutative parameter. These theta functions can be regarded as bases of the space of holomorphic homomorphisms between holomorphic line bundles over noncommutative complex tori.

12 pages

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Cited by in corpus (3)

• Categories of holomorphic line bundles on higher dimensional noncommutative complex tori
• An $A_{\infty }$-structure for lines in a plane
• Cohomology Groups of Deformations of Line Bundles on Complex Tori