2023/09/28 by Andrey Krutov, Krutov, Andrey, Dimitry Leites +3
Mathematics · Physics and Astronomy · #17B65 (Primary) 17B50 (Secondary) #58A30 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2309.16370
openalex publication_date 2023/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Under usual locality assumptions, we classify all non-integrable distributions with simple infinite-dimensional Lie superalgebra of symmetries over ℂ: we single out 15 series (containing 2 analogs of contact series and one family of deformations of their divergence-free subalgebras), and 7 exceptional Lie superalgebras. Over algebraically closed fields~\mathbbK of characteristic p>0, we classify the W-gradings (corresponding to a maximal subalgebra of finite codimension) of the known simple vectorial Lie (super)algebras with unconstrained shearing vector of heights of the indeterminates, distinguish W-gradings of (super)algebras preserving non-integrable distributions. For p>3, we get analogs of the result over ℂ. For p=3, of all possible W-gradings (12 of Skryabin algebras, 3 of superized Melikyan algebras, and 4 of Bouarroudj superalgebras) most are new, together with the corresponding distributions. For p=2, we also get several new examples of distributions and their Lie (super)algebras of symmetries.