# Kac-Moody algebras in M-theory

@article{Buyl2006KacMoodyAI, title={Kac-Moody algebras in M-theory}, author={Sophie de Buyl}, journal={arXiv: High Energy Physics - Theory}, year={2006} }

In this thesis, we consider several aspects of over-extended and very-extended Kac-Moody algebras in relation with theories of gravity coupled to matter. In the first part, we focus on the occurrence of KM algebras in the cosmological billiards. We analyse the billiards in the simplified situation of spatially homogeneous cosmologies. The most generic cases lead to the same algebras as those met in the general inhomogeneous case, but also sub-algebras of the "generic" ones appear. Next, we…

## 12 Citations

### Connections between Kac-Moody algebras and M-theory

- Mathematics
- 2007

We investigate some of the motivations and consequences of the conjecture that the Kac-Moody algebra E11 is the symmetry algebra of M-theory, and we develop methods to aid the further investigation…

### Case for support Unitary forms of Kac – Moody algebras and Kac – Moody groups

- Mathematics
- 2009

The proposed project is set in pure mathematics within the areas of infinite-dimensional Lie theory and geometric group theory. Its goal is to contribute to the structure theory of unitary forms…

### Coxeter group structure of cosmological billiards on compact spatial manifolds

- Mathematics
- 2008

We present a systematic study of the cosmological billiard structures of Einstein-p-form systems in which all spatial directions are compactified on a manifold of nontrivial topology. This is…

### Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4

- Mathematics
- 2009

We study the symmetries of pure N=2 supergravity in D=4. As is known, this theory reduced on one Killing vector is characterised by a non-linearly realised symmetry SU(2,1) which is a non-split real…

### STRINGS AND MEMBRANES FROM EINSTEIN GRAVITY, MATRIX MODELS AND W∞ GAUGE THEORIES AS PATHS TO QUANTUM GRAVITY

- Physics
- 2008

It is shown how w∞, w1+∞ gauge field theory actions in 2D emerge directly from 4D gravity. Strings and membranes actions in 2D and 3D originate as well from 4D Einstein gravity after recurring to the…

### Generalized spin representations

- Mathematics
- 2015

We introduce the notion of a generalized spin representation of the maximal compact subalgebra $\mathfrak k$ of a symmetrizable Kac--Moody algebra $\mathfrak g$ in order to show that, if defined over…

### ON E(11) OF M-THEORY: 1. HIDDEN SYMMETRIES OF MAXIMAL SUPERGRAVITIES AND LEGO OF DYNKIN DIAGRAMS

- Physics
- 2007

th in physics of strong interactions, when the study of hidden symmetries was very efficient in classifying various resonances. It resulted in the QCD foundation in the end, with the well-defined…

### Hidden Symmetries of M-Theory and Its Dynamical Realization

- Mathematics
- 2008

We discuss hidden symmetries of M-theory, its feedback on the construction of the M-theory effective action, and a response of the effective action when locality is pre- served. In particular, the…

### Generalized spin representations. Part 1: Reductive finite-dimensional quotients of maximal compact subalgebras of Kac-Moody algebras

- Mathematics
- 2011

We introduce the notion of a generalized spin representation of the maximal compact subalgebra k of a symmetrizable Kac–Moody algebra g in order to show that, if defined over a formally real field,…

### IWASAWA DECOMPOSITION AND VOGAN DIAGRAMS OF SOME HYPERBOLIC KAC-MOODY ALGEBRAS

- Mathematics
- 2013

This paper constructs the Vogan diagrams for hyperbolic Kac- Moody algebras. We also construct the Iwasawa decomposition of real forms of Kac-Moody group in relation with Vogan diagrams, which have…

## References

SHOWING 1-10 OF 168 REFERENCES

### Hyperbolic Kac Moody algebras and Einstein billiards

- Mathematics
- 2004

We identify the hyperbolic Kac Moody algebras for which there exists a Lagrangian of gravity, dilatons, and p-forms which produces a billiard that can be identified with their fundamental Weyl…

### Einstein billiards and overextensions of finite-dimensional simple Lie algebras

- Mathematics, Physics
- 2002

In recent papers, it has been shown that (i) the dynamics of theories involving gravity can be described, in the vicinity of a spacelike singularity, as a billiard motion in a region of hyperbolic…

### Higher-order M-theory corrections and the Kac–Moody algebra E10

- Mathematics
- 2005

It has been conjectured that the classical dynamics of M-theory is equivalent to a null geodesic motion in the infinite-dimensional coset space E10/K(E10), where K(E10) is the maximal compact…

### The symmetry of M-theories

- Mathematics
- 2003

We consider the Cartan subalgebra of any very extended algebra Script G+++ where Script G is a simple Lie algebra and let the parameters be space-time fields. These are identified with diagonal…

### From very-extended to overextended gravity and M-theories

- Mathematics
- 2005

The formulation of gravity and M-theories as very-extended Kac-Moody invariant theories encompasses, for each very-extended algebra G+++, two distinct actions invariant under the overextended…

### Subalgebras of Hyperbolic Kac-Moody Algebras

- Mathematics
- 2003

The hyperbolic (and more generally, Lorentzian) Kac-Moody (KM) Lie algebras A of rank r+2 > 2 are shown to have a rich structure of indefinite KM subalgebras which can be described by specifying a…

### COSMOLOGICAL SINGULARITIES, EINSTEIN BILLIARDS AND LORENTZIAN KAC–MOODY ALGEBRAS

- Physics, Mathematics
- 2005

The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of…

### Cosmological backgrounds of superstring theory and solvable algebras: oxidation and branes

- Mathematics
- 2004

### Kac-Moody symmetries of ten-dimensional non-maximal supergravity theories

- Mathematics, Physics
- 2004

A description of the bosonic sector of ten-dimensional N = 1 supergravity as a non-linear realisation is given. We show that if a suitable extension of this theory were invariant under a Kac-Moody…