# Poincaré and sl(2) algebras of order 3

@article{Goze2006PoincarAS, title={Poincar{\'e} and sl(2) algebras of order 3}, author={Michel Goze and Michel Rausch de Traubenberg and Adrian Tanasa}, journal={Journal of Mathematical Physics}, year={2006}, volume={48}, pages={093507-093507} }

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 sl(2,C) and iso(1, 3) the Poincare 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.

## 22 Citations

### About Filiform Lie Algebras of Order 3

- Mathematics
- 2015

The aim of this work is to review recent advances in generalizing filiform Lie (super)algebras into the theory of Lie algebras of order F. Recall that the latter type of algebras constitutes the…

### HIGHER-ORDER EXTENSIONS OF THE POINCARÉ ALGEBRA

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- 2012

Cubic extensions of the Poincare algebra can be constructed in consistency with physical assumptions, and provide new insights for the description of phenomena. In this paper we review some recent…

### Parafermions for higher order extensions of the Poincaré algebra and their associated superspace

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- 2009

Parafermions of orders 2 and 3 are shown to be the fundamental tool to construct superspaces related to cubic and quartic extensions of the Poincaré algebra. The corresponding superfields are…

### Some Results on Cubic and Higher Order Extensions of the Poincare Algebra

- Mathematics
- 2008

In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincare algebra. We first give some general properties of Lie superalgebras with some emphasis on…

### Cubic extentions of the Poincaré algebra

- Mathematics
- 2006

A systematic study of nontrivial cubic extensions of the Poincare algebra in four dimensions is undertaken. Explicit examples are given with various techniques (Young tableau, characters, etc.).

### Ternary algebras and groups

- Mathematics
- 2007

We construct explicitly groups associated to specific ternary algebras which extend the Lie (super)algebras (called Lie algebras of order three). It turns out that the natural variables which appear…

### Fractional Supersymmetric iso(1,1)

- Mathematics
- 2018

In this study, fractional supersymmetric iso(1,1) based on the permutation groups S3, formulated in the Hopf algebra is obtained. This algebra is denoted by U 32(iso(1,1)) .

### Color Lie algebras and Lie algebras of order F

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- 2008

The notion of color algebras is generalized to the class of F-ary algebras, and corresponding decoloration theorems are established. This is used to give a construction of colored structures by means…

### Split Lie algebras of order 3

- MathematicsJournal of Algebra and Its Applications
- 2019

We introduce the class of split Lie algebras of order 3 as the natural generalization of split Lie superalgebras and split Lie algebras. By means of connections of roots, we show that such a split…

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