대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제47권5호
  • /
  • Pages.997-1000
  • /
  • 2010
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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SOME REDUCED FREE PRODUCTS OF ABELIAN C*

  • Heo, Jae-Seong (DEPARTMENT OF MATHEMATICS RESEARCH INSTITUTE FOR NATURAL SCIENCES HANYANG UNIVERSITY) ;
  • Kim, Jeong-Hee (DEPARTMENT OF MATHEMATICS RESEARCH INSTITUTE FOR NATURAL SCIENCES HANYANG UNIVERSITY)
  • 투고 : 2009.03.25
  • 발행 : 2010.09.30
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초록

We prove that the reduced free product of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras is not the minimal tensor product of reduced free products of $k\;{\times}\;k$ 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 $II_1$-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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참고문헌

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