$F-$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 $F>2$.
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],
[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA],
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
@article{hal-00023339,
author = {Rausch De Traubenberg, Michel and Slupinski, Marcus J.},
title = {Finite-dimensional Lie algebras of order F},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00023339}
}
Rausch De Traubenberg, Michel; Slupinski, Marcus J. Finite-dimensional Lie algebras of order F. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00023339/