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 language | English |
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Pages (from-to) | 329-338 |
Number of pages | 10 |
Journal | Mathematical Notes |
Volume | 76 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - Sept 2004 |
Externally published | Yes |
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)