Some properties of a class of diagonalizable states of von Neumann algebras

N. N. Ganikhodzhaev, F. M. Mukhamedov

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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 III λ, where λ ε (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 III 1. It is shown that, for a certain class of Hamiltonians, there exists a unique translation-invariant ground state.

Original languageEnglish
Pages (from-to)329-338
Number of pages10
JournalMathematical Notes
Volume76
Issue number3-4
DOIs
Publication statusPublished - Sep 2004
Externally publishedYes

Keywords

  • Connes spectrum
  • Markov state
  • associated representation
  • diagonalizable state
  • factor of type iii
  • translation-invariant ground state
  • von Neumann algebra

ASJC Scopus subject areas

  • Mathematics(all)

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