Symmetries and half-sided modular inclusions of von Neumann algebras |
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Authors: | Hans-Werner Wiesbrock |
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Institution: | (1) Institut für Theoretische Physik, FU Berlin, Germany |
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Abstract: | LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by ,
N
,
N the modular operators to (, ), (N, ), resp (N , ). Assume now
-it
N
it
N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups
it
,
N
ir
,
N
is
,t, r, s generate a unitary representation of the group S1(2, )/Z
2 of positive energy.Another result is related to two half-sided modular inclusions (1 , ) and (2 , ). Under proper conditions the three modular groups
it
,
1
ir
,
2
is
,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik. |
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Keywords: | 81T05 |
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