Polyvector Super-Poincare Algebras
Abstract
A class of Z2-graded Lie algebra and Lie superalgebra extensions of the pseudo-orthogonal algebra of a spacetime of arbitrary dimension and signature is investigated. They have the form g = g0 + g1, with g0 = so(V) + W0 and g1 = W1, where the algebra of generalized translations W = W0 + W1 is the maximal solvable ideal of g, W0 is generated by W1 and commutes with W. Choosing W1 to be a spinorial so(V)-module (a sum of an arbitrary number of spinors and semispinors), we prove that W0 consists of polyvectors, i.e. all the irreducible so(V)-submodules of W0 are submodules of V. We provide a classification of such Lie (super)algebras for all dimensions and signatures. The problem reduces to the classification of so(V)-invariant k V-valued bilinear forms on the spinor module S.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.