This article is cited in 3 papers

Some Properties of a Class of Diagonalizable States of von Neumann Algebras

N. N. Ganikhodzhaev, F. M. Mukhamedov

National University of Uzbekistan named after M. Ulugbek

Abstract: In this paper, a class of representations of uniformly hyperfinite algebras is constructed and the corresponding von Neumann algebras are studied. It is proved that, under certain conditions, the Markov states generate factors of type $\operatorname{III}_\lambda$, where $\lambda\in(0,1)$, in the GNS representation; this gives a negative answer to the conjecture that the factors corresponding to Hamiltonians with nontrivial interactions have type $\operatorname{III}_1$. It is shown that, for a certain class of Hamiltonians, there exists a unique translation-invariant ground state.

UDC: 517.98

Received: 17.06.2001
Revised: 20.11.2003

DOI: 10.4213/mzm111

 English version: Mathematical Notes, 2004, 76:3, 329–338

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