Contractions of Filippov algebras

Sep, 2010
25 pages
Published in:
  • J.Math.Phys. 52 (2011) 013516
e-Print:
Report number:
  • FTUV-10-0901,
  • IFIC-10-29

Citations per year

2011201320152017201910
Abstract: (arXiv)
We introduce in this paper the contractions Gc\mathfrak{G}_c of nn-Lie (or Filippov) algebras G\mathfrak{G} and show that they have a semidirect structure as their n=2n=2 Lie algebra counterparts. As an example, we compute the non-trivial contractions of the simple An+1A_{n+1} Filippov algebras. By using the \.In\'on\'u-Wigner and the generalized Weimar-Woods contractions of ordinary Lie algebras, we compare (in the G=An+1\mathfrak{G}=A_{n+1} simple case) the Lie algebras LieGc\,\mathfrak{G}_c (the Lie algebra of inner endomorphisms of Gc\mathfrak{G}_c) with certain contractions (LieG)IW(\mathrm{Lie}\,\mathfrak{G})_{IW} and (LieG)WW(\mathrm{Lie}\,\mathfrak{G})_{W-W} of the Lie algebra LieG\,\mathfrak{G} associated with G\mathfrak{G}.
Note:
  • 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 This v3 is actually v2 (v1 had been replaced by itself by error).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
  • 02.20.Sv
  • Lie algebras