JONES TYPE C^(*)-BASIC CONSTRUCTION IN NON-EQUILIBRIUM HOPF SPIN MODELS  

作　　者：魏晓敏 蒋立宁 Xiaomin WEI;Lining JIANG(School of Physical and Mathematical Sciences,Nanjing Tech University,Nanjing 211816,China;School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]School of Physical and Mathematical Sciences,Nanjing Tech University,Nanjing 211816,China [2]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China

出　　处：《Acta Mathematica Scientia》2023年第6期2573-2588,共16页数学物理学报（B辑英文版）

基　　金：supported by the NSFC (11871303).

摘　　要：Let H be a finite dimensional Hopf C^(*)-algebra,and let K be a Hopf^(*)-subalgebra of H.Considering that the field algebra■K of a non-equilibrium Hopf spin model carries a D(H,K)-invariant subalgebra ■K,this paper shows that the C^(*)-basic construction for the inclusion ■K×■K can be expressed as the crossed product C^(*)-algebra■KD(H,K).Here,D(H,K)is a bicrossed product of the opposite dual H^(op) and K.Furthermore,the natural action of D(H,K)on D(H,K)gives rise to the iterated crossed product■KD(H,K)×D(H,K),which coincides with the C^(*)-basic construction for the inclusion■K×■KD(H,K).In the end,the Jones type tower of field algebra■Kis obtained,and the new field algebra emerges exactly as the iterated crossed product.

关 键 词：field algebra conditional expectation basic construction C*-tower 

分 类 号：O15[理学—数学]