대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제53권1호
  • /
  • Pages.163-180
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  • 2016
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON THE STRUCTURE OF GRADED LIE TRIPLE SYSTEMS

  • 투고 : 2015.01.08
  • 발행 : 2016.01.31
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초록

We study the structure of an arbitrary graded Lie triple system $\mathfrak{T}$ with restrictions neither on the dimension nor the base field. We show that $\mathfrak{T}$ is of the form $\mathfrak{T}=U+\sum_{j}I_j$ with U a linear subspace of the 1-homogeneous component $\mathfrak{T}_1$ and any $I_j$ a well described graded ideal of $\mathfrak{T}$, satisfying $[I_j,\mathfrak{T},I_k]=0$ if $j{\neq}k$. Under mild conditions, the simplicity of $\mathfrak{T}$ is characterized and it is shown that an arbitrary graded Lie triple system $\mathfrak{T}$ is the direct sum of the family of its minimal graded ideals, each one being a simple graded Lie triple system.

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피인용 문헌

  1. On the structure of graded Leibniz triple systems vol.496, 2016, https://doi.org/10.1016/j.laa.2016.01.043