Irrational Rotation Algebra as a Crossed Product

Authors

  • Sareh Haghkhah
  • Masoumeh Faghih Ahmadi

DOI:

https://doi.org/10.30495/jme.v0i0.26

Keywords:

Partial action, partial homeomorphism, crossed product, rotation algebra, topologically free

Abstract

In this paper we will consider the crossed product C(T ) ×α Z, where T is the unit circle, α(n) = αn is a rotation through the angle −2πnθ for n ∈ Z, and θ is a fixed irrational number. We will apply some results about patial actions to repre- sent this crossed product as a C∗-subalgebra of B(L2(T)). Also, by a different method form the proof of Davidson, we show that this crossed product is isomorphic to the irrational rotation algebra.

Author Biographies

Sareh Haghkhah

Islamic Azad University - Sepidan Branch Sepidan, Iran

Masoumeh Faghih Ahmadi

Islamic Azad University - Sepidan Branch Sepidan, Iran

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Published

2006-01-01

Issue

Vol 1 (2006-2007)

Section

Vol. 1, No. 1, (2006)

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