| Co-Investigator(Kenkyū-buntansha) |
NAKAI Eiichi Osaka Kyoiku University, Faculty of education, Assistant Professor, 教育学部, 助教授 (60259900)
FUJII Masatoshi Osaka Kyoiku University, Faculty of education, Professor, 教育学部, 教授 (10030462)
KATAYAMA Yoshikazu Osaka Kyoiku University, Faculty of education, Professor, 教育学部, 教授 (10093395)
SADASUE Gaku Osaka Kyoiku University, Faculty of education, Lecturer, 教育学部, 講師 (40324884)
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| Research Abstract |
1. In the reduced free product of C^*-algebras, (A,φ) = (A_1, φ_1) * (A_2,φ_2) with respect to faithful states φ_1 and φ_2, A is purely infinite and simple if A_1 is a reduced crossed product B ×_<a,r> G for G an infinite group, if φ_1 is well behaved with respect, to this crossed product decomposition, if A_2 ≠ C and if φ is not a trace.
2. It is shown that for two dynamical approximation entropies (one C^* and one W^*) the implementing inner automorphism in a crossed product A ×_α Z has the same entropy value as the automorphism α. Using the techniques, in the proof, an example of a highly ergodic non-asymptotically abelian automorphism with topological entropy zero is also given. More specifically, it is shown that the free shifts on the Cuntz algebra Ο_∞ and the reduced free group C^*-algebra C^*_γ(F∞) have topological entropy zero.
3. We defined an entropic invariant for automorphisms on amenable groups and investigated basic properties. Related results were obtained by Broen-Germain independently at the same time.
4. We showed that the free group factor L(F_m) has a continuous family of non conjugate outer actions of GL(n,Z) for all m = 2, 3, ・・・, ∞, and give an estimation of the Connes-Stormer entropy for each automorphism appearing in the actions. By restricting them to subgroups with Kazhdan's property T (for an example SL(n, Z)), we have a continuous family of non co-cycle conjugate outer actions on L(F_m),m 【greater than or equal】 2.
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