On the notion of relative property (T) for inclusions of von Neumann algebras

ON THE NOTION OF RELATIVE PROPERTY (T) FOR INCLUSIONS OF VON NEUMANN ALGEBRAS by JESSE PETERSON and SORIN POPA*

We prove that the notion of rigidity (or relative property (T)) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no “continuity constants” are required. The notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras with countable decomposable center was introduced in ([P1]) by requiring that one of the ...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.

Inclusions of Von Neumann Algebras and Quantum Groupoïds Iii

In a former article, in collaboration with Jean-Michel Vallin, we have constructed two ”quantum groupöıds” dual to each other, from a depth 2 inclusion of von Neumann algebrasM0 ⊂ M1, in such a way that the canonical Jones’tower associated to the inclusion can be described as a tower of successive crossed-products by these two structures. We are now investigating in greater details these struct...

INCLUSIONS OF VON NEUMANN ALGEBRAS, AND QUANTUM GROUPOÿIDS II

In a former article, in collaboration with Jean-Michel Vallin, we have constructed two ”quantum groupoÿıds” dual to each other, from a depth 2 inclusion of von Neumann algebras M0 ⊂ M1. We are now investigating in greater details these structures : in the previous article, we had constructed the analog of a co-product, and in this paper, are defined a co-inverse, by making the polar decompositi...