#
Classification of irrational Θ-deformed CAR C*-algebras
Journal article, 2021

a_i*a_i+a_ia_i*=1,

a_i*a_j=e^{2πiΘij}a_ja_i*,

a_ia_j=e^{−2πiΘij}a_ja_i.

We prove that CARΘ has a C(Kn)-structure, where Kn=[0,1/2]^n is the hypercube and describe the fibers. We classify irreducible representations of CARΘ in terms of representations of higher-dimensional noncommutative tori. We prove that for a given irrational Θ1 there are only finitely many Θ2 such that CARΘ1≃CARΘ2. Namely, CARΘ1≃CARΘ2 implies (Θ1)ij=±(Θ2)σ(i,j)modZ for a bijection σ of the set {(i,j):i<j, i,j=1,…,n}. For n=2 it means that CARθ1≃CARθ2 iff θ1=±θ2modZ.

C*-algebra, non-commutative torus, Riefell deformation

## Author

### Olexiy Kuzmin

Chalmers, Mathematical Sciences, Analysis and Probability Theory

### Lyudmyla Turowska

Chalmers, Mathematical Sciences, Analysis and Probability Theory

#### Münster Journal of Mathematics

1867-5778 (ISSN) 1867-5786 (eISSN)

Vol. 14 11 559-583### Roots

Basic sciences

### Subject Categories

Mathematical Analysis

### DOI

10.17879/06089640368