Classification of irrational Θ-deformed CAR C*-algebras
Preprint, 2020

Given a skew-symmetric matrix Θ we consider the universal enveloping C*-algebra CARΘ of the ∗-algebra generated by a_1,…,a_n subject to relations
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

Roots

Basic sciences

Subject Categories

Mathematical Analysis

More information

Created

12/11/2020