Projections in rotation algebras and theta functions

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Abstract

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*.

Original languageEnglish (US)
Pages (from-to)325-357
Number of pages33
JournalCommunications in Mathematical Physics
Volume202
Issue number2
DOIs
StatePublished - Apr 1999
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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