A Galois Correspondence for Compact Groups of Automorphisms of von Neumann Algebras with a Generalization to Kac Algebras

A Galois Correspondence for Compact Groups of Automorphisms of von Neumann Algebras with a Generalization to Kac Algebras

Let M be a factor with separable predual and G a compact group of automorphisms of M whose action is minimal, i.e. M ′ ∩M = C, where M denotes the G-fixed point subalgebra. Then every intemediate von Neumann algebra M ⊂ N ⊂ M has the form N = M for some closed subgroup H of G. An extension of this result to the case of actions of compact Kac algebras on factors is also presented. No assumptions...

fixed point property for banach algebras associated to locally compact groups

در این پایان نامه به بررسی خاصیت نقطه ثابت و خاصیت نقطه ثابت برای نیم گروههای برگشت پذیر چپ روی بعضی جبرهای باناخ از جمله جبر فوریه و جبر فوریه استیلتیس پرداخته شده است. برای مثال بیان شده است که اگر گروه یک گروه فشرده موضعی با همسایگی فشرده برای عنصر همانی که تحت درونریختی ها پایاست باشد آنگاه جبر فوریه و جبر فوریه استیلتیس دارای خاصیت نقطه ثابت برای نیم گروه های برگشت پذیر چپ است اگر و تنها ا...

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

Institute for Mathematical Physics Compact Kac Algebras and Commuting Squares Compact Kac Algebras and Commuting Squares Compact Kac Algebras and Commuting Squares Compact Kac Algebras and Commuting Squares

3 We consider commuting squares of nite dimensional von Neumann algebras having the algebra of complex numbers in the lower left corner. Examples include the vertex models, the spin models (in the sense of subfactor theory) and the commuting squares associated to nite dimensional Kac algebras. To any such commuting square we associate a compact Kac algebra and we compute the corresponding subfa...

On Pairs of Automorphisms of Von Neumann Algebras

Let e,8 be *-automorphlsms of avon Neumann algebra M satisfying the operator equation -I -I + =+8 In this paper we prove a general decomposition theorem in the non-commuting situation as compared to the usual commuting case (see references) and prove that there exists a central projection p in M such that 2 82 on Mp and 2 8-2 on M(l-p). KEYS WORDS AND PHRASES. Automorphlsms, central projections...