Correa da Silva R (2026)
Publication Type: Book chapter / Article in edited volumes
Publication year: 2026
Publisher: Springer Science and Business Media Deutschland GmbH
Series: Trends in Mathematics
Book Volume: Part F2224
Pages Range: 307-315
DOI: 10.1007/978-3-032-21578-9_26
The aim of this work is to review and tie together ideas from recent joint works with G. Lechner and L. Giorgetti in which we introduce a family of von Neumann algebras, called twisted Araki–Woods algebras, generalizing free Bose and Fermion field theories within Algebraic Quantum Field Theory. These algebras are constructed from standard subspaces and a bounded operator T acting as a twist, encoding deformations of Fock space statistics. We show that the vacuum is cyclic and separating for these algebras precisely when T satisfies the Yang–Baxter equation and crossing symmetry. Finally, we study inclusions of such algebras, providing conditions under which the relative commutant yields either an irreducible inclusion or type III factor.
APA:
Correa da Silva, R. (2026). Twisted Araki–Woods Algebras: Structure and Inclusions. In (pp. 307-315). Springer Science and Business Media Deutschland GmbH.
MLA:
Correa da Silva, Ricardo. "Twisted Araki–Woods Algebras: Structure and Inclusions." Springer Science and Business Media Deutschland GmbH, 2026. 307-315.
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