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We prove that the reduced free product of k × k matrix algebras over abelian C*-algebras is not the minimal tensor product of reduced free products of k × 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 Ⅱ1-factors and solidity of free product Ⅱ1-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 Ⅱ1-factors. Finally, we give a free product factor which is not solid in the weak sense.
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참고문헌 (16)
참고문헌 신청
A. Connes / 1980 / A factor of type II1 with countable fundamental group / J. Operator Theory 4 (1) : 151 ~ 153
A. Connes / 1985 / Property T for von Neumann algebras / Bull. London Math. Soc. 17 (1) : 57 ~ 62
A. Nica / 2006 / Lectures on the Combinatorics of Free Probability / Cambridge University Press
A. Valette / 1994 / Old and new about Kazhdan's property (T). in: Representations of Lie groups and quantum groups / Longman Sci. Tech. : 271 ~ 333
D. Avitzour / 1982 / Free products of C*-algebras / Trans. Amer. Math. Soc. 271 (2) : 423 ~ 435
A. Connes / 1985 / Property T for von Neumann algebras / Bull. London Math. Soc. 17 (1) : 57 ~ 62
A. Nica / 2006 / Lectures on the Combinatorics of Free Probability / Cambridge University Press
A. Valette / 1994 / Old and new about Kazhdan's property (T). in: Representations of Lie groups and quantum groups / Longman Sci. Tech. : 271 ~ 333
D. Avitzour / 1982 / Free products of C*-algebras / Trans. Amer. Math. Soc. 271 (2) : 423 ~ 435
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