Structures Preserved by Consistently Graded Lie Superalgebras

Abstract

Dual Pfaff equations (of the form \tilde D^a = 0, \tilde D^a some vector fields of degree -1) preserved by the exceptional infinite-dimensional simple Lie superalgebras ksle(5|10), vle(3|6) and mb(3|8) are constructed, yielding an intrinsic geometric definition of these algebras. This leads to conditions on the vector fields, which are solved explicitly. Expressions for preserved differential form equations (Pfaff equations), brackets (similar to contact brackets) and tensor modules are written down. The analogous construction for the contact superalgebra k(1|m) (a.k.a. the centerless N=m superconformal algebra) is reviewed.