Analogues of the exponential map associated with complex structures on noncommutative two-tori

Details Analogues of the exponential map associated with complex structures on noncommutative two-tori Analogues of the exponential map associated with complex structures on noncommutative two-tori

2004-04-03

arxiv.org/abs/math/0404056v4

Mathematics

Quantum Algebra

AMSLatex, 23 pages, minor corrections

Scientific paper

We define and study analogues of exponentials for functions on noncommutative two-tori that depend on a choice of a complex structure. The major difference with the commutative case is that our noncommutative exponentials can be defined only for sufficiently small functions. We show that this phenomenon is related to the existence of certain discriminant hypersurfaces in an irrational rotation algebra. As an application of our methods we give a very explicit characterization of connected components in the group of invertible elements of this algebra.

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