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Cyclic Cohomology of Non-Commutative Tori

Published online by Cambridge University Press:  20 November 2018

Ryszard Nest
Ryszard Nest*
Affiliation:
University of Copenhagen, Copenhagen, Denmark
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In this paper we shall compute the cyclic cohomology of a non-commutative torus, i.e., a certain algebra associated with an antisymmetric bicharacter of a finite rank free abelian group G.

The main result is

1.1

where

The method of computation generalises the computation of the cyclic cohomology of the irrational rotation algebras given by Connes in [3]. (Our method works equally well also in the rational case, which was dealt with by a different method by Connes in [3].)

We first describe the Hochschild cohomology of in an explicit way, and then combine this description with the exact sequence of [3]:

1.2

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 5 , 01 October 1988 , pp. 1046 - 1057
Copyright
Copyright © Canadian Mathematical Society 1988

References

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