2012/10/17 by Junsheng Fang, Chunlan Jiang, Fang, Junsheng +5
Materials Science · Mathematics · #46L35 #47C15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Lanthanide and Transition Metal Complexes #Operator Algebras (math.OA) #math.OA #msc:46L35 #msc:47C15
paper · pdf · doi:10.48550/arxiv.1210.4771
51 pages
arxiv created 2012/10/17 · openalex publication_date 2012/10/17 · arxiv updated 2012/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a class of generalized universal irrational rotation C^*-algebras Aθ,γ=C^*(x,w) which is characterized by the relations w^*w=ww^*=1, x^*x=γ(w), xx^*=γ(e-2πiθw), and xw=e-2πiθwx, where θ is an irrational number and γ(z)∈ C(\mathbbT) is a positive function. We characterize tracial linear functionals, simplicity, and K-groups of Aθ,γ in terms of zero points of γ(z). We show that if Aθ,γ is simple then Aθ,γ is an A\mathbb T-algebra of real rank zero. We classify Aθ,γ in terms of θ and zero points of γ(z). Let Aθ=C^*(u,v) be the universal irrational rotation C^*-algebra with vu=e2πiθuv. Then C^*(u+v)≅ Aθ,|1+z|2. As an application, we show that C^*(u+v) is a proper simple C^*-subalgebra of Aθ which has a unique trace, K1(C^*(u+v))≅ ℤ, and there is an order isomorphism of K0(C^*(u+v)) onto ℤ+ℤθ. Moreover, C^*(u+v) is a unital simple A\mathbb T-algebra of real rank zero. We also calculate the spectrum and the Brown measure of u+v.