Related papers: On $E_{10}$ and the DDF construction
In this paper we review the coset construction for winding subalgebras of affine Lie algebras. We classify all cosets of central charge $\hat c<1$ and calculate their branching rules. The corresponding character identities give certain…
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 algebra, then this algebra would have to…
The Lorentzian Kac-Moody algebra E11, obtained by doubly overextending the compact E8, is decomposed into representations of its canonical hyperbolic E10 subalgebra. Whereas the appearing representations at levels 0 and 1 are known on…
In this paper we study the systematics of the affine extension of supergravity duality algebras when we step down from D=4 to D=2. For all D=4 supergravities (with N >= 3) there is a universal field theoretical mechanism promoting the…
Over-extended Kac-Moody algebras contain so-called gradient structures - a gl(d)-covariant level decomposition of the algebra contains strings of modules at different levels that can be interpreted as spatial gradients. We present an…
In this thesis we summarize the reformulation of the bosonic sector of eleven dimensional supergravity as a simultaneous nonlinear realisation based on the conformal group and an enlarged affine group called G11. The vielbein and the gauge…
The conjecture of a hidden $E_{10}$ symmetry of M-theory is supported by the close connection between the dynamics of D=11 supergravity near a spacelike singularity and a truncation of an one-dimensional $\sigma$-model with $E_{10}$…
We discuss the higher dimensional generalizations of the Virasoro and Affine Kac-Moody Lie algebras. We present an explicit construction for a central extensions of the Lie Algebra $Map (X, \g)$ where $\g$ is a finite-dimensional Lie…
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 of this idea. The definitions required to…
Starting from the very-extended Kac-Moody algebra $E_{11}$, we consider the algebra $E_{11,D}^{local}$, obtained by adding to the non-negative level $E_{11}$ generators the $D$-dimensional momentum operator and an infinite set of additional…
A Kac-Moody algebra is called hyperbolic if it corresponds to a generalized Cartan matrix of hyperbolic type. We study root subsystems of root systems of hyperbolic algebras. In this paper, we classify maximal rank regular hyperbolic…
The interaction of a Lie algebra $\LL,$ having a weight space decomposition with respect to a nonzero toral subalgebra, with its corresponding root system forms a powerful tool in the study of the structure of $\LL.$ This, in particular,…
In conformal field theories, when the conformal symmetry is enhanced by a global Lie group symmetry, the original Virasoro algebra can be extended to Kac-Moody algebra. In this paper, we extend the lattice construction of the Kac-Moody…
An affine vertex operator construction at arbitrary level is presented which is based on a completely compactified chiral bosonic string whose momentum lattice is taken to be the (Minkowskian) affine weight lattice. This construction is…
The dual space of the Cartan subalgebra in a Kac-Moody algebra has a partial ordering defined by the rule that two elements are related if and only if their difference is a non-negative or non-positive integer linear combination of simple…
In the conjectured correspondence between supergravity and geodesic models on infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the constraints play a central role. We present a Sugawara-type construction in terms…
We completely classify and give explicit descriptions of the maximal closed subroot systems of real affine root systems. As an application we describe a procedure to get the classification of all regular subalgebras of affine Kac Moody…
We look to gradations of Kac-Moody Lie algebras by Kac-Moody root systems with finite dimensional weight spaces. We extend, to general Kac-Moody Lie algebras, the notion of C-admissible pair as introduced by H. Rubenthaler and J. Nervi for…
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 chamber. Because of the invariance of the…
We consider a natural generalisation of the class of hyperbolic Kac-Moody algebras. We describe in detail the conditions under which these algebras are Lorentzian. We also construct their fundamental weights, and analyse whether they…