scholarly journals Abelian subalgebras of von Neumann algebras

1971 ◽  
Vol 0 (110) ◽  
pp. 0-0 ◽  
Author(s):  
Donald Bures
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann ◽  
Abelian Subalgebras

On C*-Diagonals

1986 ◽  
Vol 38 (4) ◽  
pp. 969-1008 ◽  
Author(s):  
Alexander Kumjian
Keyword(s):  
Equivalence Relation ◽  
Cohomology Class ◽  
Cartan Subalgebra ◽  
Von Neumann Algebras ◽  
Topological Invariant ◽  
Full Generality ◽  
Von Neumann ◽  
Abelian Subalgebras ◽  
Analogous Question ◽  
Definition Of

Preface. The impetus for this study arose from the belief that the structure of a C*-algebra is illuminated by an understanding of the manner in which abelian subalgebras embed in it. Posed in its full generality, the question concerning abelian subalgebras would seem impossible to answer. A notion of diagonal subalgebra is, however, proposed which has the virtue that one can associate a “topological”; invariant to the pair consisting of the diagonal and the ambient algebra, from which these algebras may be retrieved.In the setting of von Neumann algebras, the analogous question was addressed in the seminal work of Feldman and Moore [13]. Their definition of Cartan subalgebra permits the abstraction of a complete invariant consisting of a Borel equivalence relation together with a certain cohomology class on the relation from which the Cartan pair may be recovered. Our development parallels theirs in spirit; differences in substance derive from the topological flavor of C*-theory.

Lectures on von Neumann Algebras

2019 ◽  
Author(s):  
Serban-Valentin Stratila ◽  
Laszlo Zsido
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann

scholarly journals Amalgamated free product rigidity for group von Neumann algebras

2018 ◽  
Vol 329 ◽  
pp. 819-850 ◽  
Author(s):  
Ionuţ Chifan ◽  
Adrian Ioana
Keyword(s):  
Free Product ◽  
Von Neumann Algebras ◽  
Von Neumann ◽  
Amalgamated Free Product
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