# Contractions of Filippov algebras - Mathematical Physics

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Abstract: We introduce in this paper the contractions $\mathfrak{G} c$ of $n$-Lie orFilippov algebras $\mathfrak{G}$ and show that they have a semidirectstructure as their $n=2$ Lie algebra counterparts. As an example, we computethe non-trivial contractions of the simple $A {n+1}$ Filippov algebras. Byusing the \.In\-on\-u-Wigner and the generalized Weimar-Woods contractions ofordinary Lie algebras, we compare in the $\mathfrak{G}=A {n+1}$ simple casethe Lie algebras Lie$\,\mathfrak{G} c$ the Lie algebra of inner endomorphismsof $\mathfrak{G} c$ with certain contractions$\mathrm{Lie}\,\mathfrak{G} {IW}$ and $\mathrm{Lie}\,\mathfrak{G} {W-W}$ ofthe Lie algebra Lie$\,\mathfrak{G}$ associated with $\mathfrak{G}$.

Autor: J.A. de Azcarraga, J.M. Izquierdo, M. Picon

Fuente: https://arxiv.org/