Related papers: Galilean free Lie algebras
A lot of developments made during the last years show that Kac-Moody algebras play an important role in the algebraic structure of some supergravity theories. These algebras would generate infinite-dimensional symmetry groups. The possible…
Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…
Many recent researches indicate that several gravitational D-dimensional theories suitably coupled to some matter fields (including in particular pure gravity in D dimensions, the low energy effective actions of the bosonic string and the…
We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible In\"on\"u--Wigner…
We study some applications of solvable Lie algebras in type IIA, type IIB and M theories. RR and NS generators find a natural geometric interpretation in this framework. Special emphasis is given to the counting of the abelian nilpotent…
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also…
We describe an infinite-dimensional algebra of hidden symmetries for the self-dual gravity equations. Besides the known diffeomorphism-type symmetries (affine extension of w(infinity) algebra), this algebra contains new hidden symmetries,…
Vacuum gravitational fields invariant for a bidimensional non Abelian Lie algebra of Killing fields, are explicitly described. They are parameterized either by solutions of a transcendental equation (the tortoise equation) or by solutions…
We find a first--order partial differential equation whose solutions are all ultralocal scalar combinations of gravitational constraints with Abelian Poisson brackets between themselves. This is a generalisation of the Kucha\v{r} idea of…
$F-$Lie algebras are natural generalisations of Lie algebras (F=1) and Lie superalgebras (F=2). When $F>2$ not many finite-dimensional examples are known. In this paper we construct finite-dimensional $F-$Lie algebras $F>2$ by an inductive…
In this work, we expand the hidden $AdS$-Lorentz superalgebra underlying $D=4$ supergravity, reaching a (hidden) Maxwell superalgebra. The latter can be viewed as an extension involving cosmological constant of the superalgebra underlying…
This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…
The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3…
Divergence-free Lie algebras (also known as the special Lie algebras of Cartan type) are Lie algebras of volume-preserving transformation groups. They are simple in generic case. Dokovic and Zhao found a certain graded generalization of…
We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our…
A general construction of integrable hierarchies based on affine Lie algebras is presented. The models are specified according to some algebraic data and their time evolution is obtained from solutions of the zero curvature condition. Such…
Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpretation of Cartan's method of equivalence via reduction and…
We discuss a new formalism for constructing a non-relativistic (NR) theory in curved background. Named as galilean gauge theory, it is based on gauging the global galilean symmetry. It provides a systematic algorithm for obtaining the…
Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as $W$-algebras. Known examples include contractions of pairs of the Virasoro algebra, its $N=1$…
We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative…