The Entire Cyclic Cohomology of Noncommutative 2-Tori

TL;DR

This paper computes the entire cyclic cohomology of noncommutative 2-tori, showing it is isomorphic to their periodic cyclic cohomology, based on their algebraic structure as inductive limits of subhomogeneous $F^*$-algebras.

Contribution

It provides the first explicit computation of the entire cyclic cohomology for noncommutative 2-tori, linking it to their algebraic structure as inductive limits.

Findings

Entire cyclic cohomology is isomorphic to periodic cyclic cohomology for noncommutative 2-tori.

Noncommutative 2-tori are inductive limits of subhomogeneous $F^*$-algebras.

The algebraic structure clarifies their cyclic cohomology properties.

Abstract

Our aim in this paper is to compute the entire cyclic cohomology of noncommutative 2-tori. First of all, we clarify their algebraic structure of noncommutative 2-tori as a $F^*$-algebra, according to the idea of Elliott-Evans. Actually, they are the inductive limit of subhomogeneous $F^*$-algebras. Using such a result, we compute their entire cyclic cohomology, which is isomorphic to their periodic one as a complex vector space.