Project/Area Number  09640189 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Okayama University 
Principal Investigator 
KAJIWARA Tsuyoshi Okayama Univ., Dept.Envir.and Math.Sciences, Associate Professor, 環境理工学部, 助教授 (50169447)

CoInvestigator(Kenkyūbuntansha) 
SASAKI Toru Okayama University., Dept.Envir.and Math.Sciences, Lecturer, 環境理工学部, 講師 (20260664)
HIRAI Yasuhisa Okayama Univ., Dept.Education, Associate Professor, 教育学部, 助教授 (70156636)
IKEHATA Shuichi Okayama Univ., Dept.Envir.and Math.Sciences, Professor, 環境理工学部, 教授 (20116429)
ISHIKAWA Hirofumi Okayama Univ., Dept.Envir.and Math.Sciences, Professor, 環境理工学部, 教授 (00108101)
NAKAJIMA Atushi Okayama Univ., Dept.Envir.and Math.Sciences, Professor, 環境理工学部, 教授 (30032824)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,500,000 (Direct Cost : ¥2,500,000)
Fiscal Year 1998 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1997 : ¥1,500,000 (Direct Cost : ¥1,500,000)

Keywords  Hilbert bimodule / Crossed product / dynamical system / Simplicity / ヒルベルト双加群 / 接合積 / 力学系 / 単純性 / C^*algebra / crossed product 
Research Abstract 
1. We define crossed product C*bimodule by finite group, and obtain some fundamental results. Moreover, we study AD duality in operator algebra theory by this method. These results are published in "Crossed products of Hilbert *Cbimodules by countable discrete groups". 2. We define crossed product C*bimodule by bundles over finite groups, and prove the associativity law for multiple crossed products. These results are published in "Crossed products of Hilbert C*bimodule by bundles. 3. We investigate ideal structures of C*algebras associated with finitely generated Hilbert C*bimodules over unital C*algebras A.We define the condition (I) and show the simplicity under this condition. Moreover we define the condition (11) and under this condition we present the correspondence the ideals in the bimodules algebras and the ideals of A.We present some examples satisfying these conditions. These results are published in "Ideal structure and simplicity of the C*algebra generated b9Hilbert bimodules". 4. We define coaction on finitely generated Hilbert C*bimodule by finite groups. We show that resulting crossed product is made into a finitely generated Hilbert C*bimodule. This results is published in "Coaction crossed products of Hubert C*bimodule by finite groups". 5. We define Hilbert C*bimodules for countable continuous graphs whose components are 1dimensional torus, and study the structure of associated C*algebras. We obtain simplicity and ideal structure of these algebras. These results are published in "Hilbert C*bimodules and countably infinite continuous graphs" 6. We are studying singular dynamical system using Hilbert C*bimodule method. We construct natural basis for the bimodule associated with the tent map. We are plan to. define conjugacy invariant for the above dynamical systems using our method.
