• Title/Summary/Keyword: free product of $C^*$-algebras

Search Result 3, Processing Time 0.022 seconds

SOME REDUCED FREE PRODUCTS OF ABELIAN C*

  • Heo, Jae-Seong;Kim, Jeong-Hee
    • Bulletin of the Korean Mathematical Society
    • /
    • v.47 no.5
    • /
    • pp.997-1000
    • /
    • 2010
  • 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.

FREE PROBABILITY THEORY AND ITS APPLICATION

  • Heo, Jaeseong
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.15 no.2
    • /
    • pp.13-23
    • /
    • 2003
  • We prove a simplicity of the $C^*$-algebra generated by some $C^*$-subalgebra and a Haar unitary in a free product of finite von Neumann algebras. Some examples and questions are given.

  • PDF