Journal of Operator Theory

Volume 68, Issue 2, Fall 2012 pp. 443-462.

The entire cyclic cohomology of noncommutative 2-tori

Authors: Katsutoshi Kawashima
Author institution: Department of Liberal Arts, Kurume National College of Technology, Kurume, Fukuoka, 830--8555, Japan

Summary: 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 an $F^*$-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.

Keywords: Entire cyclic cohomology, Fr\'echet $*$-algebras, noncommutative tori

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