A 1-cohomology characterization of property (T) in von Neumann algebras

We obtain a characterization of property (T) for von Neumann algebras in terms of 1-cohomology, similar to the Delorme-Guichardet theorem for groups.

[1]  S. Popa,et al.  On the Notion of Relative Property (T) for Inclusions of Von Neumann Algebras , 2004, math/0402417.

[2]  J. Sauvageot,et al.  Derivations as square roots of Dirichlet forms , 2003 .

[3]  S. Popa.  On a class of type $II_1$ factors with Betti numbers invariants , 2002, math/0209130.

[4]  R. Speicher,et al.  Operator-valued distributions. I. Characterizations of freeness , 2001, math/0201001.

[5]  Dan Voiculescu,et al.  The Analogues of Entropy and of Fisher's Information Measure in Free Probability Theory: VI. Liberation and Mutual Free Information , 1999 .

[6]  Correspondences , 1998, Cerebrovascular Diseases.

[7]  D. Voiculescu.  The analogues of entropy and of Fisher's information measure in free probability theory V. Noncommutative Hilbert Transforms , 1998 .

[8]  D. Voiculescu.  The analogues of entropy and of Fisher's information measure in free probability theory, I , 1993 .

[9]  E. Davies,et al.  Non-commutative symmetric Markov semigroups , 1992 .

[10]  C. Akemann,et al.  Unbounded Negative Definite Functions , 1981, Canadian Journal of Mathematics.

[11]  Erik Christensen,et al.  Cohomology of Operator Algebras and Quantum Dynamical Semigroups , 1979 .

[12]  A. Guichardet.  Etude de la 1-cohomologie et de la topologie du dual pour les groupes de Lie à radical Abelien , 1977 .

[13]  David E. Evans.  CONDITIONALLY COMPLETELY POSITIVE MAPS ON OPERATOR ALGEBRAS , 1977 .

[14]  岸本 晶孝.  Dissipations and Derivations (冨田-竹崎理論とその応用) , 1976 .

[15]  A. Connes,et al.  Classification of Injective Factors Cases II 1 , II ∞ , III λ , λ 1 , 1976 .

[16]  G. Lindblad.  On the generators of quantum dynamical semigroups , 1976 .

[17]  E. Effros.  Property Γ and inner amenability , 1975 .

[18]  P. Jolissaint.  On property (T) for pairs of topological groups , 2005 .

[19]  J. Sauvageot.  Quantum dirichlet forms, differential calculus and semigroups , 1990 .

[20]  J. Sauvageot.  Tangent bimodule and locality for dissipative operators on C*-algebras , 1989 .

[21]  A. Connes,et al.  Property T for von Neumann Algebras , 1985 .

[22]  Robert J. Zimmer,et al.  Kazhdan’s Property (T) , 1984 .

[23]  Theworkof Alain Connes.  CLASSIFICATION OF INJECTIVE FACTORS , 1981 .

[24]  P. Delorme.  1-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus de représentations , 1977 .

[25]  D. Kazhdan.  Connection of the dual space of a group with the structure of its close subgroups , 1967 .

[26]  J. Neumann,et al.  On Rings of Operators. III , 1940 .