For each α ∈ (0, 1), Aα denotes the universal C*-algebra generated by two unitaries u and v, which satisfy the commutation relation uv = e2πiαvu. We consider the order four automorphism σ of Aα defined by σ(u) = v, σ(v) = u-1 and describe a method for constructing projections in the fixed point algebra Aσ α, using Rieffel's imprimitivity bimodules and Jacobi's theta functions. In the case α = q-1, q ∈ Z, q ≥ 2, we give explicit formulae for such projections and find a lower bound for the norm of the Harper operator u + u* + v + v*.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics