GENERALIZED SIMPLE NONCOMMUTATIVE TORI  

作　　者：C. G. PARKDepartment of Mathematics, Chungnam National Uinversity, Taejon 305-764, South Korea. 

出　　处：《Chinese Annals of Mathematics,Series B》2002年第4期539-544,共6页数学年刊（B辑英文版）

基　　金：Project supported by Grant No.1999-2-102-001-3 from the Interdisciplinary Research Program Year of the KOSEF.

摘　　要：The generalized noncommutative torus Tkp of rank n was defined in [4] by the crossed product Am/k ×a3 Z ×a4 … ×an Z, where the actions ai of Z on the fibre Mk(C) of a rational rotation algebra Am/k are trivial, and C*(kZ × kZ) ×a3 Z ×a4 ... ×an Z is a completely irrational noncommutative torus Ap of rank n. It is shown in this paper that Tkp is strongly Morita equivalent to Ap, and that Tkp (?) Mp∞ is isomorphic to Ap (?) Mk(C) (?) Mp∞ if and only if the set of prime factors of k is a subset of the set of prime factors of p.

关 键 词：Noncommutative torus Equivalence bimodule UHF-algebra Cuntz algebra Crossed product 

分 类 号：O177.5[理学—数学]