Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11012932 | Journal of Functional Analysis | 2018 | 36 Pages |
Abstract
Let θ,θⲠbe irrational numbers and A,B be matrices in SL2(Z) of infinite order. We compute the K-theory of the crossed product AθâAZ and show that AθâAZ and Aθâ²âBZ are â-isomorphic if and only if θ=±θâ²(modZ) and IâAâ1 is matrix equivalent to IâBâ1. Combining this result and an explicit construction of equivariant bimodules, we show that AθâAZ and Aθâ²âBZ are Morita equivalent if and only if θ and θⲠare in the same GL2(Z) orbit and IâAâ1 is matrix equivalent to IâBâ1. Finally, we determine the Morita equivalence class of AθâF for any finite subgroup F of SL2(Z).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Christian Bönicke, Sayan Chakraborty, Zhuofeng He, Hung-Chang Liao,