Lie algebras of order F and extensions of the Poincare algebra

摘要

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 Poincare algebra by an Inonii-Wigner contraction of a certain F-Lie algebras with F > 2.