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dc.contributor.authorKruglikov, Boris
dc.contributor.authorSanti, Andrea
dc.contributor.authorThe, Dennis
dc.date.accessioned2021-03-04T10:15:06Z
dc.date.available2021-03-04T10:15:06Z
dc.date.issued2020-10-23
dc.description.abstractWe 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 superalgebras associated with two particular choices of parabolics. We discuss non-holonomic superdistributions with growth vector (2|4, 1|2, 2|0) deforming the flat model SHC, and prove that the second Spencer cohomology group gives a binary quadratic form, thereby indicating a “square-root” of Cartan's classical binary quartic invariant for generic rank 2 distributions in a 5-dimensional space. Finally, we obtain super-extensions of Cartan's classical submaximally symmetric models, compute their symmetries and observe a supersymmetry dimension gap phenomenon.en_US
dc.identifier.citationKruglikov, Santi, The. G(3)-supergeometry and a supersymmetric extension of the Hilbert–Cartan equation. Advances in Mathematics. 2020en_US
dc.identifier.cristinIDFRIDAID 1846099
dc.identifier.doi10.1016/j.aim.2020.107420
dc.identifier.issn0001-8708
dc.identifier.issn1090-2082
dc.identifier.urihttps://hdl.handle.net/10037/20646
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.relation.journalAdvances in Mathematics
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2020 The Author(s)en_US
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410en_US
dc.titleG(3)-supergeometry and a supersymmetric extension of the Hilbert–Cartan equationen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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