Irrational Rotation Algebra as a Crossed Product

Sareh Haghkhah, Masoumeh Faghih Ahmadi

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.

Keywords


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

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