Complex structures on Three-point space

Abstract

We discuss notions of almost complex, complex and Kähler structures in the realm of non-commutative geometry and investigate them for a class of finite dimensional spectral triples on the three-point space. We classify all the almost complex structures on this non-commutative manifold, which also turn out to be complex structures, but none of them are Kähler in our sense.

arXiv commentThis is an old article written in 2017 and it appeared in print only recently. It forms a short section of the first author's thesis