Work

Decompositions of Hyperbolic Kac–Moody Algebras with Respect to Imaginary Root Groups

Year: 2024

Type: article

Abstract: We propose a novel way to define imaginary root subgroups associated with (timelike) imaginary roots of hyperbolic Kac–Moody algebras. Using in an essential way the theory of unitary irreducible representation of covers of the group SO(2, 1), these imaginary root subgroups act on the complex Kac–Moody algebra viewed as a Hilbert space. We illustrate our new view on Kac–Moody groups by considering the example of a rank-two hyperbolic algebra that is related to the Fibonacci numbers. We also point out some open issues and new avenues for further research, and briefly discuss the potential relevance of the present results for physics and current attempts at unification.

Source: Communications in Mathematical Physics

DOI: 10.1007/s00220-024-05107-2

Authors: Alex J. Feingold, Axel Kleinschmidt, Hermann Nicolai

Institutions: Binghamton University, Max Planck Institute for Gravitational Physics

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890

Funders: European Commission, HORIZON EUROPE European Research Council