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arXiv 1009.0372math-phhep-thmath.MPmath.QAmath.RA
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Filippov代数的压缩

Contractions of Filippov algebras

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

备注：
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 This v3 is actually v2 (v1 had been replaced by itself by error).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
发表信息：
J.Math.Phys.52:013516,2011
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摘要：

本文引入了$n$ -李（或Filippov）代数$\mathfrak{G}$的压缩$\mathfrak{G}_c$，并证明了它们与对应的$n=2$李代数一样具有半直结构.作为例子，我们计算了简单$A_{n+1}$ Filippov代数的非平凡压缩.利用普通李代数的Lennönü-Wigner压缩和广义Weimar-Woods压缩，我们比较了（在$\mathfrak{G}=A_{n+1}$简单情形下）李代数Lie $\,\mathfrak{G}_c$（$\mathfrak{G}_c$的内自同态的李代数）与关联于$\mathfrak{G}$的李代数Lie $\,\mathfrak{G}$的某些压缩$(\mathrm{Lie}\,\mathfrak{G})_{IW}$和$(\mathrm{Lie}\,\mathfrak{G})_{W-W}$.

英文摘要：

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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