Local actions of PN, the group of finite permutations on N, on quasi-local algebras are defined and proved to be PN-abelian. It turns out that invariant states under local actions are automatically even, and extreme invariant states are strongly clustering. Tail algebras of invariant states are shown to obey a form of the Hewitt and Savage theorem, in that they coincide with the fixed-point von Neumann algebra. Infinite graded tensor products of C∗-algebras, which include the CAR algebra, are then addressed as particular examples of quasi-local algebras acted upon PN in a natural way. Extreme invariant states are characterized as infinite products of a single even state, and a de Finetti theorem is established. Finally, infinite products of factorial even states are shown to be factorial by applying a twisted version of the tensor product commutation theorem, which is also derived here.
De Finetti-type theorems on quasi-local algebras and infinite Fermi tensor products
Crismale V.
;Rossi S.;Zurlo P.
2023-01-01
Abstract
Local actions of PN, the group of finite permutations on N, on quasi-local algebras are defined and proved to be PN-abelian. It turns out that invariant states under local actions are automatically even, and extreme invariant states are strongly clustering. Tail algebras of invariant states are shown to obey a form of the Hewitt and Savage theorem, in that they coincide with the fixed-point von Neumann algebra. Infinite graded tensor products of C∗-algebras, which include the CAR algebra, are then addressed as particular examples of quasi-local algebras acted upon PN in a natural way. Extreme invariant states are characterized as infinite products of a single even state, and a de Finetti theorem is established. Finally, infinite products of factorial even states are shown to be factorial by applying a twisted version of the tensor product commutation theorem, which is also derived here.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
