Title of article :
On C
∗-algebras generated by isometries with twisted
commutation relations
Author/Authors :
Moritz Weber، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2013
Abstract :
In the theory of C
∗-algebras, interesting noncommutative structures arise as deformations of the tensor
product, e.g. the rotation algebra Aϑ as a deformation of C(S1) ⊗ C(S1). We deform the tensor product
of two Toeplitz algebras in the same way and study the universal C
∗-algebra T ⊗ϑ T generated by two
isometries u and v such that uv = e2πiϑvu and u
∗
v = e
−2πiϑvu
∗, for ϑ ∈ R. Since the second relation
implies the first one, we also consider the universal C
∗-algebra T ∗ϑ T generated by two isometries u
and v with the weaker relation uv = e2πiϑvu. Such a “weaker case” does not exist in the case of unitaries,
and it turns out to be much more interesting than the twisted “tensor product case” T ⊗ϑ T . We show that
T ⊗ϑ T is nuclear, whereas T ∗ϑ T is not even exact. Also, we compute the K-groups and we obtain
K0(T ∗ϑ T ) = Z and K1(T ∗ϑ T ) = 0, and the same K-groups for T ⊗ϑ T .
© 2013 Elsevier Inc. All rights reserved.
Keywords :
Commutation relations , Noncommutative torus , Universal C?-algebra , Isometries , Rotation algebra , Twist
Journal title :
Journal of Functional Analysis
Journal title :
Journal of Functional Analysis