SOME REDUCED FREE PRODUCTS OF ABELIAN C*-ALGEBRAS AND SOME C*-SUBALGEBRA IN A FREE PRODUCTopen access
- Authors
- Heo, Jaeseong; Kim, Jeong Hee
- Issue Date
- Sep-2010
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- free product of C*-algebras; Powers' group; minimal tensor product; stable rank 1; prime factor; property T; Cartan subalgebra
- Citation
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.47, no.5, pp.997 - 1010
- Indexed
- SCIE
SCOPUS
KCI
- Journal Title
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
- Volume
- 47
- Number
- 5
- Start Page
- 997
- End Page
- 1010
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/174189
- DOI
- 10.4134/BKMS.2010.47.5.997
- ISSN
- 1015-8634
- Abstract
- We prove that the reduced free product of k x k matrix algebras over abelian C*-algebras is not the minimal tensor product of reduced free products of k x k matrix algebras over abelian C*-algebras. It is shown that the reduced group C*-algebra associated with a group having the property T of Kazhdan is not isomorphic to a reduced free product of abelian C*-algebras or the minimal tensor product of such reduced free products. The infinite tensor product of reduced free products of abelian C*-algebras is not isomorphic to the tensor product of a nuclear C*-algebra and a reduced free product of abelian C*-algebra. We discuss the freeness of free product Ill-factors and solidity of free product II(1)-factors weaker than that of Ozawa. We show that the freeness in a free product is related to the existence of Cartan subalgebras in free product II(1)-factors. Finally, we give a free product factor which is not solid in the weak sense.
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