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

ESI The Erwin Schr odinger

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...

Compact Kac Algebras and Commuting Squares

We consider commuting squares of finite 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 finite dimensional Kac algebras. To any such commuting square we associate a compact Kac algebra and we compute the corresponding sub...

Almost split real forms for hyperbolic Kac-Moody Lie algebras

A Borel-Tits theory was developped for almost split forms of symmetrizable Kac-Moody Lie algebras [J. of Algebra 171, 43-96 (1995)]. In this paper, we look to almost split real forms for symmetrizable hyperbolic KacMoody Lie algebras and we establish a complete list of these forms, in terms of their Satake-Tits index, for the strictly hyperbolic ones and for those which are obtained as (hyperbo...

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

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...