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 $F>2$.

20 pages, LateX

References in corpus (3)

• Fractional helicity, Lorentz symmetry breaking, compactification and anyons
• Fractional Super Lie Algebras and Groups
• Kac-Moody algebras and Lie algebras of regular vector fields on tori

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