Finite-dimensional Lie algebras of order F
Abstract
$F-$Lie algebras are natural generalisations of Lie algebras (F=1) and Lie superalgebras (F=2). When $F>2$ not many finite-dimensional examples are known. In this paper we construct finite-dimensional $F-$Lie algebras $F>2$ by an inductive process starting from Lie algebras and Lie superalgebras. Matrix realisations of $F-$Lie algebras constructed in this way from $\mathfrak{su}(n), \mathfrak{sp}(2n)$ $\mathfrak{so}(n)$ and $\mathfrak{sl}(n|m)$, $\mathfrak{osp}(2|m)$ are given. We obtain non-trivial extensions of the Poincaré algebra by Inönü-Wigner contraction of certain $F-$Lie algebras with $F>2$.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- October 2002
- DOI:
- 10.1063/1.1503148
- arXiv:
- arXiv:hep-th/0205113
- Bibcode:
- 2002JMP....43.5145R
- Keywords:
-
- 02.20.Sv;
- 02.20.Qs;
- 11.30.Pb;
- 02.10.Yn;
- Lie algebras of Lie groups;
- General properties structure and representation of Lie groups;
- Supersymmetry;
- Matrix theory;
- High Energy Physics - Theory;
- Mathematical Physics;
- Mathematics - Mathematical Physics;
- Mathematics - Representation Theory
- E-Print:
- 20 pages, LateX