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arXiv · 1009.0372

Contractions of Filippov algebras

J. A. de Azcarraga·J. M. Izquierdo·M. Picon
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Abstract

We introduce in this paper the contractions $\mathfrak{G}_c$ of $n$-Lie (or Filippov) algebras $\mathfrak{G}$ and show that they have a semidirect structure as their $n=2$ Lie algebra counterparts. As an example, we compute the non-trivial contractions of the simple $A_{n+1}$ Filippov algebras. By using the İnönü-Wigner and the generalized Weimar-Woods contractions of ordinary Lie algebras, we compare (in the $\mathfrak{G}=A_{n+1}$ simple case) the Lie algebras Lie$\,\mathfrak{G}_c$ (the Lie algebra of inner endomorphisms of $\mathfrak{G}_c$) with certain contractions $(\mathrm{Lie}\,\mathfrak{G})_{IW}$ and $(\mathrm{Lie}\,\mathfrak{G})_{W-W}$ of the Lie algebra Lie$\,\mathfrak{G}$ associated with $\mathfrak{G}$.

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BibTeXRIS

J. A. de Azcarraga, J. M. Izquierdo, M. Picon. 2011-01-11. Contractions of Filippov algebras. https://doi.org/10.1063/1.3533944

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