20 citations · 96 across the 24 of their papers we have counts for
25 papers
On 3-nondegenerate CR manifolds in dimension 7 (II): the intransitive case
Boris Kruglikov, Andrea Santi
We investigate 3-nondegenerate CR structures in the lowest possible dimension 7 and show that 8 is the maximal dimension for the Lie algebra of symmetries of such structures. The n…
On 3-nondegenerate CR manifolds in dimension 7 (I): the transitive case
Boris Kruglikov, Andrea Santi
We investigate 3-nondegenerate CR structures in the lowest possible dimension 7, and one of our goals is to prove Beloshapka's conjecture on the symmetry dimension bound for hypers…
Exceptionally simple super-PDE for
Andrea Santi, Dennis The
For the largest exceptional simple Lie superalgebra , having dimension , we provide two explicit geometric realizations as supersymmetries, namely as the symmetry su…
Killing superalgebras for lorentzian five-manifolds
Andrew Beckett, José Figueroa-O'Farrill
We calculate the relevant Spencer cohomology of the minimal Poincaré superalgebra in 5 spacetime dimensions and use it to define Killing spinors via a connection on the spinor bund…
Symmetries of supergeometries related to nonholonomic superdistributions
Boris Kruglikov, Andrea Santi, Dennis The
We extend Tanaka theory to the context of supergeometry and obtain an upper bound on the supersymmetry dimension of geometric structures related to strongly regular bracket-generat…
On Jordan classes for Vinberg's theta-groups
Giovanna Carnovale, Francesco Esposito, Andrea Santi
Popov has recently introduced an analogue of Jordan classes (packets, or decomposition classes) for the action of a theta-group (G_0,V), showing that they are finitely-many, locall…
Remarks on highly supersymmetric backgrounds of 11-dimensional supergravity
Andrea Santi
This note focuses on some properties and uses of filtered deformations in the context of D=11 supergravity. We define the concept of abstract symbol and give a strong version of th…
G(3)-supergeometry and a supersymmetric extension of the Hilbert-Cartan equation
Boris Kruglikov, Andrea Santi, Dennis The
We realize the simple Lie superalgebra G(3) as supersymmetry of various geometric structures, most importantly super-versions of the Hilbert-Cartan equation (SHC) and Cartan's invo…
Homogeneous symplectic 4-manifolds and finite dimensional Lie algebras of symplectic vector fields on the symplectic 4-space
D. Alekseevsky, A. Santi
We classify the finite type (in the sense of E. Cartan theory of prolongations) subalgebras , where is the symplectic 4-dimensional space,…
Classification of simple linearly compact Kantor triple systems over the complex numbers
Nicoletta Cantarini, Antonio Ricciardo, Andrea Santi
Simple finite dimensional Kantor triple systems over the complex numbers are classified in terms of Satake diagrams. We prove that every simple and linearly compact Kantor triple s…
On the algebraic structure of Killing superalgebras
José Figueroa-O'Farrill, Andrea Santi
We study the algebraic structure of the Killing superalgebra of a supersymmetric background of -dimensional supergravity and show that it is isomorphic to a filtered deformatio…
Killing superalgebras for Lorentzian four-manifolds
Paul de Medeiros, José Figueroa-O'Farrill, Andrea Santi
We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations…
Sasakian manifolds and M-theory
José Figueroa-O'Farrill, Andrea Santi
We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of -Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterising…
Eleven-dimensional supergravity from filtered subdeformations of the Poincaré superalgebra
José Figueroa-O'Farrill, Andrea Santi
We summarise the results of our recent paper (arXiv:1511.08737) highlighting what might be considered to be a Lie-algebraic derivation of eleven-dimensional supergravity.
Homogeneous models for Levi-degenerate CR manifolds
Andrea Santi
We extend the notion of a fundamental negatively -graded Lie algebra associated to any point of a Levi nondegenerat…
Spencer cohomology and eleven-dimensional supergravity
José Figueroa-O'Farrill, Andrea Santi
We recover the classification of the maximally supersymmetric bosonic backgrounds of eleven-dimensional supergravity by Lie algebraic means. We classify all filtered deformations o…
Homogeneous irreducible supermanifolds and graded Lie superalgebras
D. V. Alekseevsky, A. Santi
A depth one grading of a finite dimensional Lie superalgebra $…
Almost CR quaternionic manifolds and their immersibility in HP^n
Andrea Santi
We apply the general theory of codimension one integrability conditions for -structures developed in arXiv:1306.6817v3 [math.DG] to the case of quaternionic CR geometry. We obta…
A generalized integrability problem for G-Structures
Andrea Santi
Given an -dimensional manifold equipped with a -structure , there is a naturally induce…
Classification of maximal transitive prolongations of super-Poincaré algebras
Andrea Altomani, Andrea Santi
Let be a complex vector space with a non-degenerate symmetric bilinear form and an irreducible module over the Clifford algebra determined by this form. A s…
Tanaka structures modeled on extended Poincaré algebras
Andrea Altomani, Andrea Santi
Let (V,(.,.)) be a pseudo-Euclidean vector space and S an irreducible Cl(V)-module. An extended translation algebra is a graded Lie algebra m = m_{-2}+m_{-1} = V+S with bracket giv…
Super-Poincare' algebras, space-times and supergravities (II)
Andrea Santi, Andrea Spiro
The presentation of supergravity theories of our previous paper "Super-Poincare' algebras, space-times and supergravities (I)" is re-formulated in the language of Berezin-Leites-Ko…
Super-Poincare' algebras, space-times and supergravities (I)
A. Santi, A. Spiro
A new formulation of theories of supergravity as theories satisfying a generalized Principle of General Covariance is given. It is a generalization of the superspace formulation of…
Superization of Homogeneous Spin Manifolds and Geometry of Homogeneous Supermanifolds
Andrea Santi
Let M_0=G_0/H be a (pseudo)-Riemannian homogeneous spin manifold, with reductive decomposition g_0=h+m and let S(M_0) be the spin bundle defined by the spin representation Ad:H->\G…