Projections in Rotation Algebras and Theta Functions

Dedicated to Professor Marc A. Rieffel on the occasion of his 60th birthday

Abstract:For each α∈ (0,1), A α denotes the universal C *-algebra generated by two unitaries u and v, which satisfy the commutation relation uv=e 2 π i α vu. We consider the order four automorphism σ of A α defined by σ (u)=v, σ (v)=u −1 and describe a method for constructing projections in the fixed point algebra A α σ, using Rieffel's imprimitivity bimodules and Jacobi's theta functions. In the case α=q −1, qZ, 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 *.

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Received: 30 April 1998 / Accepted: 10 October 1998

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Boca, F. Projections in Rotation Algebras and Theta Functions. Comm Math Phys 202, 325–357 (1999). https://doi.org/10.1007/s002200050585

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Keywords

  • Explicit Formula
  • Commutation Relation
  • 60th Birthday
  • Theta Function
  • Harper Operator