K-theory for the simple C ∗ -algebra of the Fibonacchi Dyck system
Abstract
Let
F
be the Fibonacci matrix
[
1
11
0
]
. The Fibonacci Dyck shift is a subshsystem of the Dyck shift
D
2
constrained by the matrix
F
. Let
L
Ch(
D
F
)
be a
λ
-graph system presenting the subshift
D
F
, that is called the Cantor horizon
λ
-graph system for
D
F
. We will study the
C
∗
-algebra
O
L
Ch(
D
F
)
associated with
L
Ch(
D
F
)
. It is simple purely infinite and generated by four partial isometries with some operator relations. We will compute the K-theory of the
C
∗
-algebra. As a result, the
C
∗
-algebra is simple purely infinite and not semiprojective. Hence it is not stably isomorphic to any Cuntz-Krieger algebra.