# Lie subalgebras of the Weyl algebra. Lie algebras of order 3 and their application to cubic supersymmetry

@article{Tanasa2005LieSO, title={Lie subalgebras of the Weyl algebra. Lie algebras of order 3 and their application to cubic supersymmetry}, author={Adrian Tanasa}, journal={arXiv: High Energy Physics - Theory}, year={2005} }

In the first part we present the Weyl algebra and our results concerning its finite-dimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of deformations and contractions of these algebraic structures. We then concentrate on a particular such Lie algebra of order 3 which extends in a non-trivial way the Poincar\'e algebra, this extension being different of the supersymmetric extension. We then focus…

## 6 Citations

### Deformations, Contractions and Classification of Lie Algebras of Order 3

- Mathematics
- 2006

Lie algebras of order F (or F −Lie algebras) are possible generalisations of Lie algebras (F = 1) and Lie superalgebras (F = 2). These structures have been used to implement new non-trivial…

### Some combinatorial aspects of quantum field theory

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In this short survey we present the appearance of some combinatorial notions in quantum field theory. We first focus on topological graph polynomials (the Tutte polynomial and its multivariate…

### Poincaré and sl(2) algebras of order 3

- Mathematics
- 2007

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…

### Extension of the Poincaré Symmetry and Its Field Theoretical Implementation

- Mathematics
- 2006

We define a new algebraic extension of the Poincar\'e symmetry; this algebra is used to implement a field theoretical model. Free Lagrangians are explicitly constructed; several discussions regarding…

### Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory

- Mathematics
- 2010

We briefly review the r\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case,…

### M. Gozea , M. Rausch de Traubenberg † b and A. Tanasùa ‡ a §

- Mathematics
- 2008

In this paper we initiate a general classification for Lie algebras of order 3 and we give all Lie algebras