2025 - T1 - Representation theory and noncommutative geometry

Collection 2025 - T1 - Representation theory and noncommutative geometry

Organizer(s) Afgoustidis, Alexandre ; Aubert, Anne-Marie ; Clare, Pierre ; Frahm, Jan ; Pasquale, Angela ; Şengün, Haluk

Date(s) 06/01/2025 - 04/04/2025

linked URL https://indico.math.cnrs.fr/event/10843/

107 112

Algebraic Quantum Field Theory and causal homogeneous spaces - Part 2a/4

By Karl-Hermann Neeb

Lorentzian manifolds and their conformal compactifications provide the most symmetric models of spacetimes. The structures studied on such spaces in Algebraic Quantum Field Theory (AQFT) are so-called nets of operator algebras, i.e., to each open subset ${\mathcal O}$ of the space-time manifold one associates a von Neumann algebra ${\mathcal M}({\mathcal O})$ in such a way that a certain natural list of axioms is satisfied.

We report on an ongoing project concerned with the construction of such nets on general causal homogeneous spaces $M = G/H$.

Lecture 2: Euler elements and causal homogeneous spaces.

We explore which specific structures we need on the homogeneous space $M = G/H$ and the Lie group $G$, so that a rich supply of nets may exist. In particular, we explain how Euler elements of Lie algebras (elements defining 3-gradings) enter the picture as candidates of generators of modular groups. This leads to several families of causal homogeneous spaces such as compactly and non-compactly causal symmetric spaces and causal flag manifolds.

Information about the video

Date of recording 18/03/2025
Date of publication 18/03/2025
Institution IHP
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students, Students
Director(s) Alexandre Duplessis
Format MP4
Venue IHP - Darboux Amphitheater

Domain(s)

Operator Algebras

Bibliography

Lecture notes: https://en.www.math.fau.de/wp-content/uploads/sites/3/2025/03/qft-lect.pdf

MSC codes

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