Poincaré and sl(2) algebras of order 3

Abstract

In this paper we initiate a general classification for Lie algebras of order 3 and we give all Lie algebras of order 3 based on $\mathfrak{sl}(2,\mathbb{C})$ and $\mathfrak{iso}(1,3)$ the Poincaré algebra in four-dimensions. We then set the basis of the theory of the deformations (in the Gerstenhaber sense) and contractions for Lie algebras of order 3.

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Cited by in corpus (10)

• n-ary algebras: a review with applications
• Hopf algebras for ternary algebras
• Kinematical superalgebras and Lie algebras of order 3
• Ternary algebras and groups
• Parafermions for higher order extensions of the Poincaré algebra and their associated superspace
• Filiform Lie algebras of order 3
• Some Results on Cubic and Higher Order Extensions of the Poincaré Algebra
• Cubic extentions of the Poincaré algebra
• Unexpected Features of Supersymmetry with Central Charges
• Hidden quartic symmetry in N=2 supersymmetry