Endomorphism Semigroups and Lightlike Translations

Abstract

Borchers and Wiesbrock have demonstrated certain results concerning the one-parameter semigroups of endomorphisms of von Neumann algebras that appear as lightlike translations in the theory of algebras of local observables. These results are abstracted and analyzed as essentially operator-theoretic. Criteria are then demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms. All this is combined to establish a von Neumann-algebraic converse to the Borchers-Wiesbrock results. This analysis is then applied to questions of isotony and covariance for local algebras.

16 pages, Latex; minor corrections

References in corpus (1)

• Group Cohomology, Modular Theory and Space-time Symmetries

Cited by in corpus (2)

• Extension of the structure theorem of Borchers and its application to half-sided modular inclusions
• Local Nature of Coset Models