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SOME REDUCED FREE PRODUCTS OF ABELIAN C*
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 Title & Authors
SOME REDUCED FREE PRODUCTS OF ABELIAN C*
Heo, Jae-Seong; Kim, Jeong-Hee;
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 Abstract
We prove that the reduced free product of matrix algebras over abelian -algebras is not the minimal tensor product of reduced free products of matrix algebras over abelian -algebras. It is shown that the reduced group -algebra associated with a group having the property T of Kazhdan is not isomorphic to a reduced free product of abelian -algebras or the minimal tensor product of such reduced free products. The infinite tensor product of reduced free products of abelian -algebras is not isomorphic to the tensor product of a nuclear -algebra and a reduced free product of abelian -algebra. We discuss the freeness of free product -factors and solidity of free product -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 -factors. Finally, we give a free product factor which is not solid in the weak sense.
 Keywords
free product of -algebras;Powers` group;minimal tensor product;stable rank 1;prime factor;property T;Cartan subalgebra;
 Language
English
 Cited by
 References
1.
D. Avitzour, Free products of $C^*$-algebras, Trans. Amer. Math. Soc. 271 (1982), no. 2, 423-435.

2.
A. Connes, A factor of type $II_1$ with countable fundamental group, J. Operator Theory 4 (1980), no. 1, 151-153.

3.
A. Connes and V. Jones, Property T for von Neumann algebras, Bull. London Math. Soc. 17 (1985), no. 1, 57-62. crossref(new window)

4.
K. Dykema, Simplicity and the stable rank of some free product $C^*$-algebras, Trans. Amer. Math. Soc. 351 (1999), no. 1, 1-40. crossref(new window)

5.
L. Ge, On maximal injective subalgebras of factors, Adv. Math. 118 (1996), no. 1, 34-70. crossref(new window)

6.
L. Ge, Applications of free entropy to finite von Neumann algebras. II, Ann. of Math. (2) 147 (1998), no. 1, 143-157. crossref(new window)

7.
J. Heo, On outer automorphism groups of free product factors, Internat. J. Math. 13 (2002), no. 1, 31-41. crossref(new window)

8.
A. Nica and R. Speicher, Lectures on the Combinatorics of Free Probability, Cambridge University Press, Cambridge, 2006.

9.
N. Ozawa, Solid von Neumann algebras, Acta Math. 192 (2004), no. 1, 111-117. crossref(new window)

10.
N. Ozawa and S. Popa, Some prime factorization results for type $II_1$ factors, Invent. Math. 156 (2004), no. 2, 223-234. crossref(new window)

11.
S. Popa, Orthogonal pairs of *-subalgebras in finite von Neumann algebras, J. Operator Theory 9 (1983), no. 2, 253-268.

12.
R. Powers, Simplicity of the $C^*$-algebra associated with the free group on two generators, Duke Math. J. 42 (1975), 151-156. crossref(new window)

13.
S. Sakai, Asymptotically abelian $II_1$-factors, Publ. Res. Inst. Math. Sci. Ser. A 4 (1968/1969), 299-307.

14.
A. Valette, Old and new about Kazhdan’s property (T), Representations of Lie groups and quantum groups (Trento, 1993), 271-333, Pitman Res. Notes Math. Ser., 311, Longman Sci. Tech., Harlow, 1994.

15.
D. Voiculescu, Symmetries of some reduced free product $C^*$-algebras, Operator algebras and their connections with topology and ergodic theory, Lect. Notes in Math. 1132 (1985), 556-588. crossref(new window)

16.
D. Voiculescu, K. Dykema, and A. Nica, Free Random Variables, CRM Monograph Series, 1. American Mathematical Society, Providence, RI, 1992.