Related papers: $E_{11}$, Borcherds algebras and maximal supergrav…
Duality symmetries of supergravity theories are powerful tools to restrict the number of possible actions, to link different dimensions and number of supersymmetries and might help to control quantisation. (Hodge-Dirac-)Dualisation of gauge…
Using recent results on string on $AdS_{3}\times N^d$, where N is a d-dimensional compact manifold, we re-examine the derivation of the non trivial extension of the (1+2) dimensional-Poincar\'e algebra obtained by Rausch de Traubenberg and…
The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…
We consider a proper parabolic subalgebra p of a simple Lie algebra g and the Inonu-Wigner contraction of p with respect to its decomposition into its standard Levi factor and its nilpotent radical : this is the Lie algebra which is…
In any dimension, the positive level generators of the very-extended Kac-Moody algebra $E_{11}$ with completely antisymmetric spacetime indices are associated to the form fields of the corresponding maximal supergravity. We consider the…
We reformulate eleven-dimensional supergravity, including fermions, in terms of generalised geometry, for spacetimes that are warped products of Minkowski space with a $d$-dimensional manifold $M$ with $d\leq7$. The reformation has a…
We show how massive/gauged maximal supergravities in 11-n dimensions with SO(n-l,l) gauge groups (and other non-semisimple subgroups of Sl(n,R)) can be systematically obtained by dimensional reduction of ``massive 11-dimensional…
Super Hopf algebra structure on the function algebra on the extended quantum superspace has been defined. It is given a bicovariant differential calculus on the superspace. The corresponding (quantum) Lie superalgebra of vector fields and…
We examine the five-dimensional super-de Rham complex with $N = 1$ supersymmetry. The elements of this complex are presented explicitly and related to those of the six-dimensional complex in $N = (1, 0)$ superspace through a specific notion…
In this PhD Thesis, supersymmetry and its formulation in the context of D=11 supergravity is discussed from several perspectives. The role of generalized holonomy as a classification tool of supersymmetric supergravity solutions is…
We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model…
We introduce a numerical framework for dispersive equations embedding their underlying resonance structure into the discretisation. This will allow us to resolve the nonlinear oscillations of the PDE and to approximate with high order…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
Eleven-dimensional supergravity can be formulated in superspaces locally of the form $\mathbf X\times Y$ where $\mathbf X$ is 4D $N=1$ conformal superspace and $Y$ is an arbitrary 7-manifold admitting a $G_2$-structure. The…
The periplectic Lie superalgebra $\mathfrak{p}(n)$ is one of the most mysterious and least understood simple classical Lie superalgebras with reductive even part. We approach the study of its finite dimensional representation theory in…
Bonnor's map in General Relativity is duality between (dimensionally reduced) vacuum gravity and static truncation of electro-vacuum theory. It was used as a tool to generate an exact solution of electro-vacuum from some vacuum solution. It…
A geometrisation scheme internal to the category of Lie supergroups is discussed for the supersymmetric de Rham cocycles on the super-Minkowski group $\,\mathbb{T}\,$ which determine the standard super-$p$-brane dynamics with that target,…
The consistency of the embedding of four-dimensional SO(8) gauged N=8 supergravity into eleven-dimensional supergravity, where the internal directions are compactified on a seven-sphere, was established by de Wit and Nicolai in the 1980s.…
A family of geometries on S^7 arise as solutions of the classical equations of motion in 11 dimensions. In addition to the conventional riemannian geometry and the two exceptional Cartan-Schouten compact flat geometries with torsion, one…
Given a double vector bundle $D\to M$, we define a bigraded `Weil algebra' $\mathcal{W}(D)$, which `realizes' the algebra of smooth functions on the supermanifold $D[1,1]$. We describe in detail the relations between the Weil algebras of…