Polyvector Super-Poincare Algebras
Dmitri V. Alekseevsky, Vicente Cortés, Chandrashekar Devchand, Antoine Van Proeyen
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 ΛV. We provide a classification of such Lie (super)algebras for all dimensions and signatures. The problem reduces to the classification of so(V)-invariant Λk V-valued bilinear forms on the spinor module S.
Create a lesson
Related papers
Conformal field theory from automorphic forms on a quantum group
Dalimil Mazac
Anomaly effective actions for 4d N=1 superconformal field theories
Pantelis Panopoulos, Ioannis Papadimitriou
Exact Splitting of Amplitudes and One-Loop Integrands: A Classical Origin of Zeros
Yang Li, Laurentiu Rodina, Zhi-Zhen Wang
5-brane webs and generalised symmetries
Mohammad Akhond, Federico Carta, Sung-Soo Kim et al.
Form Factors in AdS from the Worldsheet
Luis F. Alday, Clément Virally, Xinan Zhou
Higher Integrability, Generalized Symmetries, and Partially Topological Field Theories
Luigi Alfonsi, Leron Borsten, Mehran Jalali Farahani et al.