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 *.

This is a preview of subscription content, access via your institution.

Author information



Additional information

Received: 30 April 1998 / Accepted: 10 October 1998

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Boca, F. Projections in Rotation Algebras and Theta Functions. Comm Math Phys 202, 325–357 (1999).

Download citation


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