Structures Preserved by Consistently Graded Lie Superalgebras
Abstract
Description
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.
An error in the definition of mb(3|8) has been corrected, and the paper has been greatly revised and expanded. In addition to Pfaff equations (preserved form equations), I give dual Pfaff equations (preserved vector field equations), solve the resulting conditions for the vector fields, and write down the brackets and tensor modules explicitly
An error in the definition of mb(3|8) has been corrected, and the paper has been greatly revised and expanded. In addition to Pfaff equations (preserved form equations), I give dual Pfaff equations (preserved vector field equations), solve the resulting conditions for the vector fields, and write down the brackets and tensor modules explicitly