Contractions of Filippov algebras

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 $\mathfrak{G}$.

plain latex, 36 pages. A few misprints corrected. This v3 is actually v2 (v1 had been replaced by itself by error). To appear in J. Math. Phys

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Cited by in corpus (2)

• Degenerations of Jordan Superalgebras
• Degenerations of Filippov algebras