English
norskBlar i forfatter "Santi, Andrea"
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Exceptionally simple super-PDE for F (4)
(Journal article; Tidsskriftartikkel; Peer reviewed, 2024-02-01)For the largest exceptional simple Lie superalgebra F(4), having dimension (24|16), we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second and third order respectively. -
G(3)-supergeometry and a supersymmetric extension of the Hilbert–Cartan equation
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-10-23)We realize the simple Lie superalgebra <i>G</i>(3) as supersymmetry of various geometric structures, most importantly super-versions of the Hilbert–Cartan equation (SHC) and Cartan's involutive PDE system that exhibit <i>G</i>(2) symmetry. We provide the symmetries explicitly and compute, via the first Spencer cohomology groups, the Tanaka–Weisfeiler prolongation of the negatively graded Lie ... -
On Jordan classes for Vinberg's theta-groups
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-10-23)V. L. Popov has recently introduced an analogue of Jordan classes (packets or decomposition classes) for the action of a θ-group (G0, V), showing that they are finitely-many, locally-closed, irreducible unions of G0-orbits of constant dimension partitioning V. We carry out a local study of their closures showing that Jordan classes are smooth and that their closure is a union of Jordan classes. We ... -
Symmetries of supergeometries related to nonholonomic superdistributions
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-06-06)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-generating distributions on supermanifolds and their structure reductions.
