Non-integrable distributions with simple infinite-dimensional Lie superalgebra of symmetries

Abstract: The only simple infinite-dimensional Lie algebras preserving a non-integrable distribution are the algebras of contact vector fields in odd dimensions. We formulate analogs of the above statement and prove them for (super)varieties over algebraically closed fields of any characteristic $p\geq0$.

Over fields $\mathbb{K}$ of characteristic $p>0$, we classify the Weisfeiler gradings (briefly: W-gradings), those 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.

Join work with D. Leites and I. Shchepochkina (arXiv:2309.16370)

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( paper | video )

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Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.

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