Algebraic representations of von Neumann algebras
نویسنده
چکیده
An algebraic extended bilinear Hilbert semispace H∓ is proposed as being the natural representation space for the algebras of von Neumann. This bilinear Hilbert semispace has a well defined structure given by the representation space Repsp(GLn(Lv ×Lv)) of an algebraic general bilinear semigroup GLn(Lv ×Lv) over the product of sets of completions characterized by increasing ranks. This representation space is a GLn(Lv×Lv)-bisemimodule MR⊗ML , decomposing into subbisemimodules according to the modular or internal conjugacy classes of GLn(Lv ×Lv) , and is in one-to-one correspondence with the corresponding cuspidal representation according to the Langlands global program. In this context, towers of von Neumann bisemialgebras on the bilinear Hilbert subsemispaces, of which structures are these subbisemimodules, are constructed algebraically which allows to envisage the classification of the factors of von Neumann from an algebraic point of view.
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