exceptional structures, exceptional isomorphisms
exceptional finite rotation groups:
and Kac-Moody groups:
exceptional Jordan superalgebra,
Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
A hyperbolic Kac-Moody Lie algebra in the E-series
is conjectured (e.g. Nicolai 08) to be the U-duality group (see there) of M-theory compactified to 1 dimension (see also F/M-theory on elliptically fibered Calabi-Yau 5-folds).
Lecture notes include
The fact that every simply laced hyperbolic Kac-Moody algebra is a sub Lie algebra of is due to
Discussion of as U-duality of supergravity/M-theory:
The case of E10 is discussed for bosonic degrees of freedom in
Thibault Damour, Marc Henneaux, Hermann Nicolai, and a ‘small tension expansion’ of M
theory_, Phys. Rev. Lett. 89, 221601 (2002) (arXiv:hep-th/0207267);
Axel Kleinschmidt, Hermann Nicolai, and invariant supergravity, JHEP 0407,
041 (2004) (arXiv:hep-th/0407101)
and for fermionic degrees of freedom in supersymmetric quantum cosmology in
Review includes
Hermann Nicolai, Wonders of and (2008) (pdf)
Hermann Nicolai, On Exceptional Geometry and Supergravity, talk at Gravitation, Solitons and Symmetries (pdf)
Discussion of phenomenology:
Axel Kleinschmidt, Hermann Nicolai, Standard model fermions and (arXiv:1504.01586)
Krzysztof A. Meissner, Hermann Nicolai, Standard Model Fermions and Infinite-Dimensional R-Symmetries, Phys. Rev. Lett. 121, 091601 (2018) (arXiv:1804.09606)
Krzysztof A. Meissner, Hermann Nicolai, Planck Mass Charged Gravitino Dark Matter, Phys. Rev. D 100, 035001 (2019) (arXiv:1809.01441)
Last revised on November 30, 2020 at 10:21:57. See the history of this page for a list of all contributions to it.