F-Lie algebras are natural generalisations of Lie algebras (F=1) and Lie superalgebras (F=2). We give finite dimensional examples of F-Lie algebras obtained by an inductive process from Lie algebras and Lie superalgebras. Matrix realizations of the $F-$Lie algebras constructed in this way from osp(2|m) are given. We obtain a non-trivial extension of the Poincaré algebra by an Inönü-Wigner contraction of a certain $F-$Lie algebras with $F>2$.
Publié le : 2002-07-05
Classification:
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],
[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT],
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
@article{hal-00023340,
author = {De Traubenberg, M. Rausch},
title = {Lie algebras of order F and extensions of the Poincar\'e algebra},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00023340}
}
De Traubenberg, M. Rausch. Lie algebras of order F and extensions of the Poincaré algebra. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00023340/