Structures Preserved by Consistently Graded Lie Superalgebras

2001/06/05 by T. A. Larsson, T A Larsson, Larsson, T A · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0106004

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

openalex publication_date 2001/06/05 · arxiv created 2001/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Dual Pfaff equations (of the form D^a = 0, 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.

Citations

• Symmetries of Everything

Cited by

• Exceptional Lie Superalgebras, Invariant Morphisms, and a Second-Gauged Standard Model

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